Yeah, they have the same basic meaning and 'comprehend' is usually more formal. There are a few places where you'd only use one of them specifically though. 'Reading comprehension exercises' are where you're given something to read, then asked questions to check you understood what you read. People can 'reach an understanding' when they agree on something, and if someone spoke to you in an unfamiliar language you'd say 'I don't understand' - 'I don't comprehend' sounds very strange, although it wouldn't be wrong! I think it would be best to use 'understand' most of the time. 'Comprehend' tends to be used in questions like 'can you / are you able to comprehend the importance of the situation?' - where you're asking if someone has a complete understanding of the consequences. It sounds more important and dramatic in questions.

I agree with Ravi - ''comprehend'' has a more academic/technical/formal usage. Look up the etymology of both words and the difference will be very clear.