"Impressed" describes the feeling of being happily surprised by how good something is. You say that you "are impressed" when something is better than you expected it to be (in a good way). For example:
I was impressed with how well organized the whole event was.
Some people in different areas may have strong feelings about whether to use "impressed by" or "impressed with", but there's so many different opinions about this that it's probably not important for English learners to worry about the difference between them. I personally use "impressed with ___" more often.