A "breach detection" is when sensitive, private or confidential information is disclosed or accessed by an unauthorised person (i.e. without the permission of the owner of that information).
For example, you sign up for a website and in doing so provide them with your email address, a password, your phone number and credit card details. If that website stores your information and then it gets hacked, and your information is stolen as part of that hack, this is called a data breach. The hackers could then sell your information on the dark web, along with the details of everyone else who had signed up to that website.