Firstly, winning is the best feeling there is (at least by any legal means). Addictive one too. There's a scientifically proven gender difference, which partially explains men's greater enthusiasm on competitive gaming and sports. We lucky guys can get from winning a physically euphoric testosterone rush. Gaming is a way to do that psychosomatically without considerable physical straining.
Then there's the storytelling side of many games, with the "what comes next" keeping you going. And that doesn't mean just plot and characters, but wanting to see what further visuals, music, ideas there is.
And in many genres there are, in one form or another, puzzles, riddles and mazes. There's satisfaction on solving those.
For me, as someone that prefers playing online with and against other people, it's the competition. The feeling that you get when you get the better of someone else and beat them at a game that you're good, it's amazing. It's also just something fun to do whilst you have some free time and to cure boredom.