What defines a game's "replay value"?

Replay value is simply a generic term for "What could motivate people to play the game again after playing through it once?"

Neither the time to play through or the graphics have anything to do with that.

Examples for factors that add to replay value:

• Branching story where players might play again to experience the other branches.
• Extensive character customization that might get players to try to play through using a different play style, e.g. stealth vs brute force.
• Randomization where players experience only some parts of all that the game might have to offer so they play again to maybe experience the other parts. This can also be randomized item drops in diablo-like games.

Replay value is a game's ability to be re-played. Either after death, or more importantly after victory. It generally specifically refers to how often you will pick the game up off the shelf to play it AGAIN after you've beaten it the first time. Some games, such as the Metal Gear genre, Borderlands genre, the Resident Evil genre, and many others, were actually DESIGNED to be played multiple times, and have content that reflects this. Beating the game (the first time) is just the beginning.

This can be accomplished in a myriad of ways, as everyone has something that speaks to them specifically. But many games have attempted to work replayability into their core game mechanics using methods such as:

• Keeping some or all of your levels and\or inventory and continuing again from the beginning with or without the enemies and tasks rescaled to your level.

• Starting the game again with a new playable character

• Starting the game again from a new perspective, giving you insights into previously unknown parts of the story

• Starting the game again as normal, but with a harder difficulty

• Starting the game again with the games levels mirrored to be backwards

• Multiple acheivememts to be obtained for 100% completion, some of which cannot all be gathered in one, or even several playthroughs.

• Unlocking a new game mode upon completion

• Including a online or local multiplayer experience so once the original campaign is finished there is still other people to slay play with.

• Having multiple game modes other than just multiplayer or singleplayer in the first place so there is more to do from the beginning.

• Giving the player cosmetic additions upon completions.

And many others...

Some games have great replayability without any of these qualities as well. Some games are just THAT good. There is so much content, and the story was so good, and the characters so iconic, that you just want to play it again and again, much like reading a good book or watching a good movie. The most famous game never intended to be replayed to such an extent but still was good enough to garner this form of reputation that comes to mind is Final Fantasy 7.

This is a partial answer that adds on to the 2 great answers provided by both dbemerlin & Ender.

One thing that can really add to replay value is a multiplayer mode (in addition to single player. I am specifically leaving out multiplyer-only games as they are a beast of their own). Each time you pick it up and play with your friends it will be a new experience.