A certificate usually means you are able to do something: a school certificate, a swimming certificate. It is an achievement, it shows you have the skills to do something. A licence usually gives you permission to do something, and not having the licence means you are NOT ALLOWED to do something. A driving licence is the first one I think of. It can be confusing, because owning a licence can show you have the skills to do something (i.e., to have a driving licence, you must be have the skills to drive a car), but the main difference is that you are not allowed to do something without the licence.

A licence is a written permission to do something, such as a driver's licence. A certificate certifies something to be true. For example, an institution would give you a certificate to say that you have studied there and achieved a certain grade.