An industry is a group of companies and organizations that all work on similar things. Some examples:
The auto industry is a group of companies and organizations that all work on cars, parts of cars, or other car-related products and technologies.
The computer industry is a group of companies and organizations that all work on computers or other computer-related products.
A profession is a more general term for a job. For example you could say "He is a brain surgeon so he is in the medical profession."
Profession is a tricky term though, it can be grammatically correct in a sentence but still not the right term to use. Watch when it is used and you will get a sense for when to use it.