What does the "reset quests" option do?

Solution 1:

What does the "Reset Quests" option do?

This option will clear all progress you have made with the character you use it on. You will have to play the storyline again and unlock each quest before you will be able to choose to start at that quest.

What are the conditions to have the option available?

To have the option available, your character needs to have completed all quests, including killing Diablo.

If you decide to use the option on a specific character, you will have to complete all the quests again to be able to use it again.

What are the benefits of resetting quests?

By resetting your quests, you will re-enable first-time bonus experience & rewards for quests, boss kills and such.

As an example, killing Diablo for the first time currently guarantees a legendary drop for level 60 characters. This will be re-activated after having reset your quest progress.

Solution 2:

There are a few reasons you would want to reset quests. Quest rewards after resetting are improved, although I don't know how. Someone will have to science it, whether it's extra exp/gold/items, etc.

Another thing is that resetting quests will net you a guaranteed legendary off of Diablo, the final boss. So by resetting, you can get yourself a legendary (eventually).