Small plates dining and snacking is popular in many different cultures and countries, which each has the own name for it. In Spain they are called tapas; in Venice, Italy they are cicchetti. Typically enjoyed by local residents in the early evening after work, they are meant to be light dishes - sometimes just one or two bites - to be tasted along with wine or cocktails.
Some people will make an entire meal out of going from one bar serving small plates to the next, sampling a house specialty here and here for hours. Others will enjoy these light bites before then going for a full dinner later in the evening (in much of Europe, it is typical to eat dinner much later than in America, closer to 9pm - 11pm instead of 6pm - 8pm.) Sometimes these bars serving small plates will also have a dining room for full meals as well.
Image above: Patatas bravas - a classic dish of Spanish tapas.
Restauranteurs in America generally take the small plates concept in a different direction, basing an entire, sit-down meal around small plates. Instead of ordering a standard 3-course meal (appetizer, entree, dessert), in a small plates restaurant you would order more like 4 - 7 courses in order to have a complete, filling meal. Chef Jose Garces popularized the concept in Philadelphia, Pennsylvania with his flagship Spanish tapas restaurant Amada. He then continued the concept with his other restaurants in the city, including Tinto, Chifa and Distrito, each focusing on a different regional cuisine yet always with a menu predominantly of small plates.
Other restauranteurs soon followed suit, and certainly in Philadelphia - as in other major cities - small plates restaurants are now everywhere. Gastropubs and bars are also often branching out from their typical nachos-and-burgers menus and offering more creative small plates options such as marinated vegetables, gourmet deviled eggs, house-made charcuterie and other "petite plates".