Application security
An attack where a harmful page makes a user's browser send a request to a site they are logged in to, which acts as if they asked.
Formal
A flaw in a web application that carries out a state-changing request just because it arrives with the user's cookie; since the web browser attaches that cookie by itself, a page on another site can trigger the request without the user knowing.
In plain English
Like someone slipping a signed order form into your post - the shop sees your signature and fills the order, never asking whether you meant to send it.
In practice
A case officer in a municipality is logged in to the case system and opens a link in a mail; the page quietly submits a hidden form that changes the payout account on a citizen's case, and the system accepts it because the login cookie came along.
Why it matters
The attacker never needs the password or even sees the response; a single visit to the wrong page can change an email address or password, or move money, in the user's name.