The tags that you have put on here show that you know quite a bit about it already.
As you know, the plague was spread by fleas. The fleas were carried by rats, but also by people. There were a few things that made it so easy for the plague to spread.
First, compared to previous times, there was a lot of travel by the time the plague started. That's how it got from one place to the next (it started in Asia).
Second, because it came from Asia and was a new disease, no one in Europe was at all immune and so it could spread rapidly.
Finally, people lived close together and, more importantly, had no decent sanitation. They didn't really keep clean. There were rats and fleas among them.