Reputation is added when you find a useful post. Take for example the tracker reviews section. You are interested in joining
IPT (just an example) and someone creates a review about
IPT. In this review, you find all the infos about the tracker you want to join. As such, this post is useful to you so you can hit the "thanks" button to show your appreciation instead of replying with a "hey mate, thanks for the review" which is considered to be a spam post.
iGiver is more a statistical element. It's feedback. If you take part in a giveaway and receive an invite for <insert random name> tracker, you will give an iGiver to the guy who invited you. The url that you were referring, it will be the url of the giveaway thread. I, for example, gave one invite and received one iGiver. This iGiver indicates that the invite i gave was processed and that the guy i gave the invite to, is now a member of the 'x' tracker. In other words, the invite delivery was successful.