“Dense” can mean a few different things depending on context, but they all revolve around the idea of being “thick” or “packed.”
Physical/material meaning
In science or everyday speech, something is dense if a lot of matter is packed into a small space, like lead or plutonium having a lot of mass in a small volume. People also say things like “dense fog” or “dense jungle” when something is thick and hard to see or move through.
Everyday and insult meaning
In casual conversation, calling a person “dense” usually means they are slow to understand, miss obvious hints, or do not pick up on social cues. It is often mildly insulting, similar to calling someone slow or thick-headed.
Other specialized meanings
In writing, “dense prose” means the text is packed with complex ideas or difficult language, so it takes a lot of concentration to read. In mathematics, a “dense” set is one where between any two elements you can always find another element from the same set.