A ring game is a normal poker game offered by a card room in a casino as opposed to a tournament game. In online poker ring games tend to refer to cash games or real money games, now differentiated from both tournament poker and play money or fun money tables.
Ring games can also refer to a full table, where there is a circle of players as opposed to a short-handed table. The advent of online poker has made a number of these poker definitions quite confusing, since short-handed tables are now deliberately offered by all online poker rooms. So, in the old days a table with five players would have been a few participants short of a ring, but now five player max tables are standard fare in online poker.