I don't really know what the point of rep power is but someone gives it to you for a post they've liked. It's a private thing so no-one but you can see it, unlike when you're thanked for a post.
To give it click on the scales at the bottom left of their post and a box pops up with a space for you to comment. You can write what you like, if you want them to know who sent it, don't forget to add your name at the end, if you don't want them to know, just leave it off.
Under the rep power part on the left you get coloured bits depending how much rep power you have. Thats about all I know about it. I just gave you some so you can see what happens when you get it.