Bonus quests are quests you will be given by doing an unlisted objective while already on a quest. For example, say you need to collect flowers for Juliah, that's the only objective that the quest shows you. But in Juliah's garden are giant wasps which are in the way of you collecting any flowers for her. You won't immediately be given the bonus quest for just being in the area but when you kill one of the wasps it will pop up and let you know that you are now on a bonus quest as well. Bonus quests are not required to progress the story in any way nor have I ever seen them lead to anything important.
All I have ever seen bonus quests reward was a little bit of extra xp. Depending on what the quest has you do, the amount of XP it will give you as a reward will vary. I've seen them give 1/3 the amount of the actual quest to 2x more than the actual quest. As I mentioned before, the bonus quests are never required to advance the story line so worse comes to worse if one is buggy or extremely difficult or annoying you can just skip it. Two things you should know about bonus quests first though.
First thing you should know is once you complete the mission you're on that lead you to the bonus quest, the bonus quest will disappear whether you've finished it or not. Along the same lines of that, when you finish a bonus quest there is no need to go somewhere special to turn it in. Once completed it will automatically reward you on the spot. The second thing you should know about bonus quests is how to receive them. There is no clear way to receive a bonus quest, finding one is about luck and some common sense.
See the quest "Final Stage - Freightskipper Fracas [Bonus] on that list? All bonus quests will be marked [Bonus]
Say your quest requires you to destroy 5 vials of blood. Now each vial of blood is located in a Fleshraider encampment, surrounded by Fleshraiders. Usually a bonus quest will present itself in this situation, immediately following the death of the first Fleshraider. Bonus quests come in all different forms (meaning different objectives) but most commonly I've found them to just kill the mobs in your quest area. It's never a small amount of mobs that it requires you to kill either, usually 15 to 45 of them.
As for how many bonus quests are worth doing, I'd say anywhere from 90% to 95% of them. Bonus quests are an excellent source for extra xp and are also generally extremely easy to do. The hardest thing I have ever had to do for a bonus quest was kill three elite mobs (They were the gold star ones). It was not impossible, just difficult. As far as I am concerned there should be only three reasons you skip a bonus quest. One, the quest is too difficult can you can't do it or find someone to do it with/help you. Two, the area you are in is so over camped by peopel that you just want to get the frig out of there because there is nothing to kill anyway. And finally, three, the quest is bugged.
That is pretty much everything you'd need to know about bonus quests. Just keep your eyes open and when you're in an area doing a quest, kill a few of the mobs around you to see if they initate a quest of their own. Also, keep an eye out after completing a bonus quest to see if it has a second part. Levels 1 - 10 all the bonus quests only had one part but once I got to about level 11 and started doing the guild quests I had two and even three part bonus quests.
Important bit of information: If you're looking to level as quickly as possible you will want to do every single bonus quest possible.