When you take a test you're using "working memory". Working memory is the information that you're using in your head to answer the specific question you're working on. Working memory is different than long-term memory, which is memories that you have stored in your brain but that you're not thinking about in a given moment. Working memory involves three main tasks: 1) selecting, or deciding which incoming information you want to pay attention to, 2) organizing, or manipulating information in your head to make it make sense, and 3) integrating, or pulling relevant information from long-term memory so you can organize it with the new, incoming information. As you can tell, that's a lot to be doing at once!

While the human brain can have an unlimited amount of information in its long-term memory, the amount of information it can handle in working memory is very limited. That is, you can only have so much information active in your head at once. One way that working memory is limited is by its two main channels: one for auditory information (sound) and another for visual and spatial information. It's hard to do two sound-based tasks at once, and it's also hard to do two visual/spatial tasks at once. However, it's less hard to do one visual task and one spatial task at the same time.

Now back to your question. All of these things (selecting, organizing, integrating, and the two channels) add up to make what cognitive psychologists call "cognitive load". When you have too much cognitive load, you're trying to do too much at once and your working memory can't handle it. When you're taking a difficult test, you need to use all of your limited working memory capacity to think about the problems that you're trying to answer. Anything that distracts you from the test will take up room in your working memory and prevent you from doing well on the test. Sometimes, music can do this. If you're taking a very difficult test, listening to music can reduce your working memory capacity enough that you can't figure out the problems. This is especially true if the music has lyrics. Human voices take up a LOT of room in working memory, even if you're not paying that much attention to them, or if they're singing in a different language! If the test is on something that involves thinking about how things sound, such as a test on a foreign language, then it will harm your performance even more. There are some cases where music might not be harmful, however. If the test is very easy and doesn't require a lot of working memory, then music can actually help if it puts you in a good mood (it still shouldn't have lyrics, however). Also, if the test is only spatial or visual, and doesn't require you thinking about anything sound-related, then listening to music will only crowd your sound channel, and will still leave you with room to do visual/spatial problems.