Making an impression means to leave people with a memory and opinion of who you are. You might make a good or bad impression, but they will not forget you. This is similar to 'impress', except that when you say that somebody impressed you, or was impressive, that means they made a good impression. The phrase is used intransitively.
Giving an impression is similar, but used transitively to describe the leaving of a memory and opinion about something specific. For example: my face gives an impression of what I am thinking.