First off I have to say there are several places you can find the info I am going to provide at several places on the internet since ArenaNet has gone out of their way to let everyone be fully informed about this game. This is just a short synopsis to get you thinking, if you didn't know this already.
1) Dungeons are optional so you are not forced to do them and still get all the fun you need to from the game.
2) There will be eight (8) dungeons at release of the game.
3) They will first appear starting at level 30 and continue every 10 levels till the level cap of 80.
4) There are 2 modes.
a) is the story mode which is part of your characters personal storyline which include cut scenes. Once this is completed you then unlock the next mode.
b) which is the explorable mode. You still can get some cut scenes here but not as many and take place after the story mode storyline. During this mode the group will be asked questions that determine the dynamic events that will take place and possibly the path taken in the dungeon since there are five paths that can be taken in each dungeon.
5) rewards given are tokens which are taken to certain vendors in Lion's Arch where they can be exchanged for items you wish to have. (NOTE: these items do not give the person better stats then can be done during regular game play, but provide an aesthetic for your character's appearence)
6) To ArenaNet the term "dungeons" to them is a "misnomer, since not all of them are underground." as quoted from the Guild Wars 2 article: Into the Dungeons.
Further quoting this article:
"Dungeons are optional, but are a lot of fun for players who seek a challenge. They don't interrupt your personal storyline, but can enhance that storyline."
Simply ArenaNet wants you to have fun.