to make matters worse; what's more
Adds an additional, often negative, point to what has just been said.
おまけに means 'to make matters worse' or 'what's more,' and it adds another fact to the situation you're describing. It often introduces something negative or undesirable, but it can also be used neutrally or even positively, depending on context. In conversation, it sounds a bit formal or emphatic, so you might prefer 'しかも' or 'そのうえ' in casual speech.
When you use おまけに, you're saying that the new information makes the overall situation even more intense, usually worse. For example, if your car broke down and then it started raining, you'd say おまけに雨まで降ってきた. It helps show that things are piling up.
It's a useful connector for storytelling or explaining circumstances, and it's common in written Japanese and news reports.