*heh*
The reputation system (also sometimes referred to as the "Karma System") is a way for user to indicate support or dislike of a post. You can hit the little scales (found at the bottom of left of each person's post) and choose either "I approve" or "I disapprove". You can also include a comment.
This adds to your reputation provided that the person hitting the scales has reputation to offer (must be a value over 50 points). You can see your points when you go to UserCP. That value will appear just above the reputations and Thanks you receive. The higher the number of points, the greater the number of "green balls" you'll get.
How much reputation you get from someone hitting those scales will depend on how many points someone has (the value is a percentage of their points).
Now, the Thanks Button is a variation of the Rep in that it allows individuals to give a quick "positive" rep and quick thanks for a post. This was created to lessen the simple "Thanks" posts for information. In this very supportive environment, it's taken off like wildfire (far greater than I would have imagined). I am contemplating creating a modified version of it that would be a "Hugs" (for those times you want to show support for someone when down, facing a challenge, etc.).
That said, it's up to you if you want to use it. That really is a personal choice and just because you receive "Thanks" or a positive rep from someone doesn't necessarily mean you need to do so in return.
Let me know if that helps any and if you have more questions, need something clarified or if I didn't quite answer what you were looking for.