Security testing is the process for find vulnerabulity and weaknesses of your software system so you can exploit it weakness before hackers do. These can save you for lossing senstive data, prevent unauthorized access, and avoid breaches.
The tests are done in automated and manual ways. These are auto scan, reviewing code, testing the application catch problems.
To simplify it all in one box, you can say security testing is to make your software strong against threats.