Assalaamu alaikum my dear,
(smile) I remember wondering the same when I was new on IB. And I remember reading the info in the link
http://www.islamicboard.com/faq.php?faq=website_usage#faq_reputation_system, and finding it confusing. So... basically, if someone thinks your post is really good and useful, they will want to give you some recognition of this. So they click on the little icon that looks like a sheriff's badge, which you can see at the bottom of the user's info, on the left side of the screen (on the computer, at any rate). Look under
likes received. Do you see? There is a little sheriffs badge-shaped icon on the left, and a little triangle with an exclamation mark on it next to it on the right. If you click on the sheriff's badge-shaped icon, you are asked if you approve or disapprove of the post. If you liked the post, click on approve. You can write a short message to the person you are repping (if you like. You don't have to though). If you
don't approve, you could also negatively rep someone. This is pretty rare, but it can be done.
In this way, you are showing your appreciation to the poster. You are also helping other people to evaluate the poster's reliability overall. The higher the reputation, the more likely that the poster has useful information.
The amount of rep that you can
give another person depends on a) the length of time you've been on the IB, and b) the amount of posts you've made. There are other variables, I think, too, and the exact calculation of the rep you can give is a bit mysterious. But a) and b) give you a general outline.
Incidentally, the little triangle with the exclamation mark is for flagging a post as potentially problematic, so that a mod can check it out. For instance, if someone is giving out someone's personal information, or if someone wants to incite others to do something very wrong (like kill someone), or... well, anything that seems really not right. Then the mods can get to it faster and perhaps take it down if necessary.
May Allah, the Kind, Protect you, my dear.