The “wishbone” offense is an offense that sets up like a “Y” or “wishbone.” It is primarily a running offense.
 
University of Texas Coach Darrell Royal used the offensive formation in a September 1968 game against the University of Houston. Houston Post writer Mickey Herskowitz has claimed coinage of the name “wishbone.”
 
 
Wikipedia: Wishbone formation
The wishbone formation, also known simply as ‘bone or the wishbone offense, is a play formation in American football.
 
The wishbone is primarily a running formation with one wide receiver, one tight end and three running backs behind the quarterback (who takes the snap under center). The back lined up behind the quarterback is the fullback and the other two are halfbacks (although they may be called tailbacks or I backs in some playbook terminology).
 
The wishbone is often associated with the option as this formation allows the quarterback to easily run the option to either side of the line. It is also ideal for running the Triple Option.
 
History
The wishbone was developed by Offensive Coordinator Emory Bellard under Head Coach Darrell Royal at the University of Texas in 1968. Royal directed Bellard to come up with an option offense after watching Texas A&M, running Gene Stallings’ option offense, beat Bear Bryant’s Alabama team in the Cotton Bowl the previous season. After experimenting with family members over the summer, Coach Bellard came up with the formation.
 
Coach Bellard demonstrated the formation to Darrell Royal, who quickly embraced the idea. It proved to be a wise choice: Texas tied its first game running the new offense, lost the second, and then won the next thirty straight games, leading to two National Championships using the formation.
 
It was given the name wishbone by the Houston Chronicle sportswriter Mickey Herskowitz.
 
Soonerfans.com
Re: Who Created the Wishbone?
About 1968, a University of Texas assistant named Emory Bellard (pronounced Bell-ARD) came up with the idea of lining up three backs in tight and running the triple option, and the wishbone was born.
 
Coach Bellard “broke the bone” when he coached at Mississippi State and introduced the “wing-bone”, moving one of the halfbacks up to a wing formation and frequently sending him in motion.
 
The wishbone concept is still alive, and still effective where it is run. It pops up occasionally in the form of a Stack-I, and a sort of Power-I formation called the I-bone. Air Force and Georgia Southern still run it, but mostly from a spread formation and mostly with motioning wingbacks.
 
Scholzgarten
TEXAS FOOTBALL TRIVIA
Darrell Royal called his new 1968 offense a “wishbone” offense after it was first named the “pulleybone” offense by a reporter.
 
Daily Cougar (University of Houston)
Cougars, Longhorns longtime rivals, have history of victories and losses
by Jason Paul Ramârez
(...)
Texas vs. Houston—it used to be big for the Longhorns, it used to be even bigger for the Cougars.
 
“Even today, if you ask any Houston player to pick one game, if they could win just one game all year, it would definitely be against Texas,” said former Houston Post columnist and University of Houston alumnus Mickey Herskowitz. “The Cougars always seemed to have had a score to settle with Texas, as does any school that plays them.”

But this wasn’t just any ordinary rivalry.
 
Houston vs. Texas was big.
 
Take the 1968 clash on Sept. 21 in Austin’s Memorial Stadium, for instance.
 
The two schools were meeting for just the second time in history as the game was the season opener for the Longhorns (No. 3 final ranking in Associated Press poll that season).
 
The game also marked the first time Texas employed, what was later coined, its wishbone offense.
 
“I remember myself and a bunch of other sports writers kicking around names of what to call Texas’ new offense,” Herskowitz said. “I remember looking at the way (the offensive backfield) was set up and seeing a chicken bone.
 
“I never dreamed that the term `wishbone’ would become such a huge part of college football.”
 
It did, and it was the Cougars (No. 18 final AP ranking in 1968) who helped christen it.
 
The two teams stood off to a 20-20 tie before Texas lost to Texas Tech the next week. But the Longhorns then proceeded to win 30 games in a row and two national championships before Notre Dame ended Texas’ string of luck with a 24-11 victory in the 1971 Cotton Bowl on New Year’s Day.
   
(Oxford English Dictionary)
wish-bone
1860 BARTLETT Dict. Amer. (ed. 3), Wish-Bone.
(...)
U.S. Football. Used attrib. and absol. to designate an offensive formation in which the full back lines up ahead of the half-backs in an alignment that resembles the shape of a wishbone.
1972 N.Y. Times 3 Nov. 48/2 Dartmouth’s best hope lies in shutting off Yale’s wishbone offense as engineered by Dick Jauron. 
 
24 September 1968, Odessa (TX) American, pg. 2B:
The backfield alignment resembles a “Y” with the fullback a step or so behind the quarterback and the halfbacks farther back, in line with the offensive guards.
 
25 September 1968, Port Arthur (TX) News, pg. 34:
The new Texas offense, dubbed “Homer’s Triple” in tribute to Cincinnati coach Homer Rice who designed it back in his high school coaching days, calls for the fullback to crack through the inside on almost every running play.
 
The quarterback has three options, depending on how the defense reacts.
 
He can wither give it to the fullback (Worster) going through the middle, keep the ball and go wide, or sweep wide and lateral to a halfback.
 
27 September 1968, Galveston (TX) Daily News, pg. 17:
Tech will be the second test for Royal’s new offense, which he calls a “wish-bone T”, with fullback Steve Worster up a step behind the quarterback. Royal said he was generally pleased with the new look but the Longhorns needed better execution.
 
28 September 1968, Galveston (TX) Daily News, pg. ?:
Coach Darrell Royal calls it the “Wishbone T”...
 
28 September 1968, Odessa (TX) American, pg. 4B:
LUBBOCK, Tex. (AP)—Texas Tech faces the task Saturday night of breaking up wixth-ranked Texas’ “wish-bone T” offense in the first Southwest Conference game of the season that could be a wild offensive donnybrook.
(...)
Texas Coach Darrell Royal was pleased with the debut of what he calls the “wishbone T” with fullback Steve Worster lining up a step behind quarterback Bill Bradley and with halfbacks Ted Koy and Chris Gilbert slotting themselves behind the guards.
 
29 December 1968, New York (NY) Times, pg. S2:
Gilbert is the heart of the Texas backfield, which aligns itself in the “Y” or so-called “Wishbone T” formation. The sophomore fullback, Steve Worster, in a four-point stance, places himself directly behind the quarterback, James Street, who either gives the ball to Worster for a quick pop up the middle or pitches out to Gilbert or Ted Koy.

17 August 1969, Washington (DC) Post, pg. 51:
Coach Darrell Royal’s Wishbone-T attack at the University of Texas produced a ground game second only to Houston’s nationally. Named for the split alignment of the set backs, the Wishbone is gaining many followers too, especially from those dazzled by the Longhorns’ deft 36-13 Cotton Bowl execution of Tennessee.
 
New York (NY) Times
Emory Bellard, Creator of Wishbone Offense, Dies at 83
By BRUCE WEBER
Published: February 10, 2011
Emory Bellard, the coach who was credited with introducing the wishbone formation to college football, providing the framework for many of the great running teams of the 1970s, died Thursday in Georgetown, Tex. He was 83.
(...)
Bellard (pronounced bell-ARD) spent 14 seasons as a head coach, first at Texas A&M and then at Mississippi State, but his signature contribution to football came in 1968 as an assistant at the University of Texas.
 
The Texas team had suffered through three subpar seasons, and the coach, Darrell Royal, seeking a change, asked Bellard to devise an offensive backfield scheme that would include a lead blocker and maximize the effectiveness of the team’s three strong running backs. Bellard came up with a variant of a two-back formation called the veer: the quarterback and the three runners lined up in the shape of a Y, or a wishbone, the fullback right behind the quarterback and two tailbacks split behind them.
(...)
Bellard may have invented the wishbone, but he didn’t name it. According to Royal, it was a newspaper writer, Mickey Herskowitz, who gets credit for that. In the 2005 book “Coach Royal: Conversations With a Texas Football Legend,” he recalled that after a game or two, he was asked at a news conference what the new formation was called. It didn’t have a name, he replied.
 
“I said: ‘Well, they’re kind of in the shape of a Y back there. Call it the Y.’ I mean, I didn’t care what they called it, you know. Mickey Herskowitz said: ‘That’s not very original. Why don’t you call it a wishbone? It’s in the shape of a wishbone.’ I said: ‘You got it, Mickey. It’s a wishbone.’”