When is it a good time to offer a draw in chess, and when should I accept one?
In casual play, the main reason to offer a draw is if the game is going on forever and shows no sign of concluding soon. Consider the motivation for the game. Maybe you're playing a game for fun after dinner, but at some point your wife is going to start making loud yawning noises. Maybe you're playing a grudge match with a friend, but both of you are hopeless at rook endings - which is where you've ended up. Maybe you made the mistake of starting a game with someone who takes hours to make any move. I've been in all of these situations! In these cases, achieving the win is secondary to the experience of playing the game. As soon as the experience becomes compromised, or real life starts to intrude, an escape becomes appealing.

One player may actually have an advantage, but if it's going to be necessary to grind out a difficult endgame to convert that advantage into a point, then it may not be considered worth it by the players to continue. A couple of times I have even conceded casual games that I believed I was winning, simply because I wasn't willing to continue to invest the time.

Another reason is if the players are amateurish enough that forcing a win is difficult or impossible. I once spent a frustrating afternoon watching two friends with very basic chess playing abilities circle uselessly for several hours, trying to figure out how to achieve a checkmate. It was like watching Brownian motion on a chessboard; essentially random checks with the vague hope of accidental checkmate. In the end, they gave up and declared a draw. This situation is depressingly common among the large group of casual players who possess no knowledge beyond how to move the pieces.

A final, rather dishonest reason is to protect the ego of your opponent. Too many casual players take losing at chess as a personal failure, or worse, an insult or demonstration of superiority by their opponent. If your opponent is your boss or your grandfather, and they take losing very badly, maybe a draw is a more political decision. In this case, the game is just part of a larger game - the game of maintaining workable relationships in the real world.