“Finger food” (or “finger foods”) are foods that are eaten with fingers rather than with a fork or a spoon. The “finger” foods usually contain meat and/or vegetables; dessert snacks such as cookies (where cutlery would not be expected to be used) are usually not included.
 
“For the first, some sandwiches, hard-boiled eggs, cake, fruit, all finger food” is from Horse & Hound on June 17, 1893. “Is asparagus a finger food?” was printed in the Minneapolis (MN) Journal on October 10, 1903. “Finger foods are olives…” was printed in The Sun (Baltimore, MD) on April 17, 1904. “Other ‘finger foods’ are the relishes, such as radishes, celery, olives, salted nuts, crystallized fruits and bonbons” was printed in the Pittsburg (PA) Sunday Press on December 4, 1910.
   
 
Wikipedia: Finger food
Finger food is food meant to be eaten directly using the hands, in contrast to food eaten with a knife and fork, spoon, chopsticks, or other utensils. In some cultures, food is almost always eaten with the hands; for example, Ethiopian cuisine is eaten by rolling various dishes up in injera bread. Foods considered street foods are frequently, though not exclusively, finger foods.
 
Types
In the western world, finger foods are often either appetizers (hors d’œuvres) or entree/main course items. In the Western world, examples of generally accepted finger food are miniature meat pies, sausage rolls, sausages on sticks, cheese and olives on sticks, chicken drumsticks or wings, spring rolls, miniature quiches, samosas, sandwiches, Merenda or other such based foods, such as pitas or items in buns, bhajjis, potato wedges, vol au vents, several other such small items and risotto balls (arancini). Other well-known foods that are generally eaten with the hands include hamburgers, pizza, chips, hot dogs, fruit, and bread. Dessert items such as cookies, pastries, ice cream in cones, or ice pops are often eaten with the hands but are not, in common parlance, considered finger foods.
 
(Oxford English Dictionary)
finger food  n. food suitable for eating with the fingers or served in such a way that it can conveniently be eaten without cutlery; a food of this type.
1893   Horse & Hound 17 June 368/1   For the first, some sandwiches, hard-boiled eggs, cake, fruit, all finger food.
1949   A. L. Hill Compl. Bk. Table Setting xix. 248   Asparagus used to be considered a finger food, but today, happily, the tips are cut off with the fork and eaten with it.
     
10 October 1903, Minneapolis (MN) Journal, “Correct Social Usage,” pg. 12, col. 3:
Is asparagus a finger food?
   
17 April 1904, The Sun (Baltimore, MD), “How to Eat” by Mrs. Linda Hull Larned, author of “The Hostess of Today,” pg. 13, col. 3:
Finger foods are olives, the stones are never put in the mouth; radishes, held by the stalks, dipping the ends in salt; raisins, removing seeds by hand surreptitiously; dates and prunes, like olives; pears and apples, cut into pieces and peeled; grapes, removing seeds like raisins; strawberries, when served unhulled, are treated like radishes, dipping them, however, in sugar instead of salt; and nuts and bonbons.
 
24 April 1904, San Francisco (CA) Examiner, pg. 67 (?), col. 3:
How to Eat Special Foods in the Smartest, Daintiest Manner
By Mrs. Linda Hull Larned, Author of “The Hostess of To-Day.”
(...)
FINGER FOODS are olives, ... (Same as above.—ed.)
 
27 July 1907, Nashville (TN) Tennessean, pg. 5, col. 3:
FOOD EATEN WITH THE FINGERS.
(...)
Crackers are eaten in the same way. Celery, radishes, olives, salted nuts, crystallized fruits, bonbons, all raw fruits (save berries, melons and grape fruit), artichokes and corn on the cob are finger foods, so to speak.
   
4 December 1910, Pittsburg (PA) Sunday Press, “Advice on Social Customs” by Mrs. Chester Adams, Women’s Magazine Section, pg. 3, col. 1:
EATEN WITH THE FINGERS
(...)
Crackers are eaten in the same way. Other “finger foods” are the relishes, such as radishes, celery, olives, salted nuts, crystallized fruits and bonbons.
   
Google Books
Etiquette in Society, in Business, in Politics, and at Home
By Emily Post
New York, NY: Funk & Wagnalls Company
1927
Pg. 208:
The fact that the spoon which is double the size of a teaspoon is known as nothing but a dessert spoon, is offered in further proof that “dessert” is “spoon” and not “finger” food!
   
Google Books
Table Etiquette:
Menus and Much Besides
By Mary Davoren Chambers
Boston, MA: Boston Cooking-School Magazine
1929
Pg. 8:
Bonbons. When in paper cases, bonbon and case are lifted together from the container, then the bonbon is picked out with the fingers and eaten.
Bouchees. These wee cakes and pastries are finger foods. When in paper cases treat like Bonbons
 
OCLC WorldCat record
Finger foods
Author: Chris Deshpande; Prodeepta Das
Publisher: London : A & C Black, ©1988.
Series: Friends.
Edition/Format:   Print book : Juvenile audience : English
Summary:
One of a series which is designed to reflect Britain’s multi-cultural society and to stimulate discussion in the infant classroom. This book looks at the different foods which may be eaten with the fingers, from fish and chips to channa and chapatis.
     
OCLC WorldCat record
Finger food : delicious canapés and hors d’oevres
Author: Heinz Imhof; Sonia Allison
Publisher: Slough : Foulsham, ©1992.
Series: Foulsham know how; Gourmet cookshelf.
Edition/Format:   Print book : English
 
OCLC WorldCat record
Finger food.
Publisher: Sydney : Murdoch Books, 2011.
Series: Step-by-step (McGraw-Hill Education)
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Providing meals, snacks and sweet and savoury treats for the family day in, day out, is something of a challenge, even for the most experienced cook. This title includes clear instructions and photographs that give guidance through the preparation process.