Volatility is the measure of how a game pays out.
There is usually a tradeoff between frequent payouts and high payouts. A game with high volatility will infrequently pay out large amounts (often with large, painful droughts in between), whereas a lower volatility game will pay out smaller amounts more frequently (but without the possibility of a huge win).
Low Volatility Games, like Blackjack and Jacks or Better, are good for people who want to gamble for a long time on a limited bankroll. Because they pay out small amounts frequently, you will be able to play for a while and stretch your dollar further. The downside is that you lose the potential for a big win, since most of the return comes from smaller wins.
High Volatility Games, like Roulette and Slots, are good for people who are going for a big win relative to their bankroll. Because they have the potential for a huge win, they are appealing to people looking to strike it rich. The downside is that you can also lose big, since so much of the return is tied up in big wins.