This site uses the Have I Been Pwned? API to check if passwords have been seen in a data breach. Your password itself is never sent to a third party during this check. Read about validating leaked passwords with K-Anonimity here.
I very much prefer giving users a choice when possible, so while I do check if a password is breached, I only notify you of it. You can still register with a breached password, though I strongly recommend against it, and recommend using a Password Manager.