Twitter - Favoriting A Retweet

I'm new to Twitter....I've gotten notifications where if I retweet someone's post, it shows up in notifications as "xyz favorited your retweet". Does that mean they basically favorited their own tweet?

I keep getting occasional RTs and am not sure how to 'favorite' the fact that they took the time to RT. I could reply back and say thanks but wanted to also know how others favorite an RT.

thanks.