Say this phrase after you've complained about something, in order to add a new complaint. For example:
I'm broke; I don't have a job; my girlfriend broke up with me. And to make matters worse, my mechanic just told me that my car needs a new transmission!
Senior management doesn't know what they're talking about. To make matters worse, they don't listen to us when we try to explain things to them.
"To make matters worse" expresses a feeling of rising frustration. Like in the examples above, you can either use it after a list of problems, or after a single problem.