When a site you signed up to is breached, your email address, username and sometimes your password start circulating online, often without you ever hearing about it. Have I Been Pwned is a free service that makes addresses collected from known breaches searchable and shows in seconds which breaches your email appears in.
The result tells you which accounts need a new password right away. The same site also lets you check whether a password has already been exposed, without sending the password in the clear.