A meeting is when a group of people gather to discuss a certain topic. Usually, during a meeting, everyone will be taking part in the discussion.
A conference is slightly different. At a conference, there is often one or maybe just a few people who speak. They give a speech or sometimes a presentation. Afterwards, people may have the opportunity to ask them questions during a question-answer time. When a person says "meeting," they are just talking about one event. It only last an hour or 2 or even less time. A conference can last for a few days and may include many different speakers.