Is the density of an object is how much matter contains?

Not exactly. This is a little tricky because there are different meanings of the Word density. In physics & chemistry it means how much a specific amount by volume a substance weighs. Technically it is defined as mass per unit volume. A teaspoon of Mercury weights about 14 times as much as a teaspoon of water because it's about 14 times as dense as water, or 14 times more dense (however it's clearer to say it). Mercury is more dense than iron so iron can float on a pool of mercury.

Another meaning of density is like bone density. Meaning how solid your bones are. Another is, dense fog, meaning it's hard to see through. In casual use: "My is he dense" -- meaning he doesn't understand things well.