The basic concept can be explained simple enough. While the complete story is somewhat complicated (and probably the reason you're getting voted to close as 'too broad'), I think a quick example might help
You have an account on stackoverflow, where you can upvote answers (e.g. this one). I could make a website that does a call to stackoverflow to upvote this answer in the background. So i'd link you to that site and then you automatically upvote me. That is bad!
So what just happened would be that the call (the request) was faked by me (forged) from another page (cross site).
Stackoverflow must take precautions to check that each call to the upvote-api is actually done by you from their own site, not sneakily by me (trough you).
The simplest way this can go wrong is if the upvote button was just an api post to https://stackoverflow.com/api/upvote/{id}
. If you are logged in and I have you post to that api from javascript in the background then you'd upvote and never be any wiser to it. Any good implementation tries to avoid this by doing any of the well known anti-csrf tricks (tokens for instance), but going into that would put us quite firmly into the 'too broad' category :D