Organized team activities (OTAs) are what professional football teams hold during the off-season. They are usually training sessions where teams learn the playbook and the techniques of their positions; hard-hitting is usually banned.
 
“There’s even something called organized team activity (or OTA)—best described as a relaxed ‘mini’ minicamp” was cited in print in June 1998. The “mini-camp” is another program that football teams hold during the offseason.
 
   
Wikipedia: Training camp (National Football League)
Organized team activities
Recently the NFL has let teams have off-season training sessions, officially called “organized team activities” (OTAs). Many teams use the OTAs to help develop players and make them better. These training sessions are in late April and early May. The OTAs are the only practices between the end of the previous season and the start of training camp. Players new to the NFL attend seminars and lectures organized by the NFL from mid-June to mid-July. For veteran players, they use the off-time to sponsor football camps for children, golf outings for charity, or even some family time.
 
12 June 1998, St. Louis (MO) Post-Dispatch, “Rams minicap ends final milestone of ‘offseason’” by Jim Thomas, pg. D3:
There’s even something called organized team activity (or OTA) - best described as a relaxed “mini” minicamp.
 
23 March 2000, Santa Rosa (CA)

, “Woodson accepts role as leader,”
INFORMAL GATHERING: Woodson, Russell and the majority of players on the roster have been at the team’s practice facility since Monday for what the team calls a voluntary organized team activity. The “OTA,” the popular term among the players, allows the Raiders to get a head start on introducing some of their new free agents—such as defensive end Regan Upshaw and cornerback Tory James -into their system.
 
4 June 2001, Belleville (IL) News-Democrat, “Martz likes progress of Rams,” pg. 1D:
The Rams will hold four days of Organized Team Activities—which are basically meetings and short practice sessions—before breaking for the summer.
 
New York (NY) Times
PRO FOOTBALL; Jets Lineman Injures Knee Seriously
By GERALD ESKENAZI
Published: May 30, 2002
(...)
Szott’s injury came during a session that the Jets call “organized team activities.” It is not a minicamp—the Jets have already had the one permitted by union rules. Instead, these are noncontact drills that started last week and will run through June 15.
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5 June 2002, St. Louis (MO) Post-Dispatch, “Rams hold office party” by Jim Thomas, pg. E1:
The Rams have four days of what’s called organized team activity (OTAs, for short) this week and next. Those are short, light practice sessions, usually about 80 minutes in duration.
 
Google Books
Vermeil:
The Essence Of Leadership
By Jeff Gordon
St. Louis, MO: Stellar Press
2003
Pg. 219:
“I thought we had very good organized team activities, the 12 of them we had in our off-season program. ”
   
17 August 2003, Santa Rosa (CA) Press Democrat, “Raiders nearly inury-free as they break camp in Napa” by Phil Barber:
Said coach Bill Callahan: “We’ve been so impressed with Donny Green, through all the OTAs (organized team activities) and minicamps.”
     
NFL.com
Unlocking the mystery of OTAs
Published: May 14, 2013 at 09:24 a.m. | 83,743 Views
03:52 – Want to know what players actually are doing at organized team activities? Eric Davis breaks down OTAs and the impact they have on rookies and veterans.