Bitcoin dominance is like the king of the crypto hill - it's the percentage of the total cryptomarket cap that belongs to Bitcoin.
It's kind of like if you were at a party, and everyone was talking about how cool they were - but then the host walked in, and suddenly everyone realized they were just a bunch of wannabes. That's what Bitcoin's like - it's the biggest, baddest crypto there is, and all the altcoins are just trying to bask in its glory.
Example
"Bitcoin dominance has been pretty steady lately, hovering around 60%. But just wait until the next bull run - it'll probably shoot up faster than a rocket to the moon."