A Ring Game is just a normal table full of people playing poker. The action goes around in a circle, with player taking turns being the "dealer" (acting last.) Players can buy-in for chips at any time and join the game. Players can also cash out their chips and leave at any time (between hands.)
Contrast with TournamentPoker.
Tournaments and ring games require different strategies. In a ring game, the chips have a dollar value, and every hand should be played so as to maximize long-term profit in chips. In a tournament, the chips have no dollar value; winnings are paid for finishing placement, so each hand should be played so as to ensure survival for as long as possible (to get a higher finishing spot.) In a ring game, if you fold out of a hand, you can not profit. In a tournament, if you fold out of a hand, and one of the people still involved goes broke and drops out of the tournament, you do profit, because your position in the finishing order has improved.