What does it mean to say the momentum is conserved?

It means if you take the initial system and calculate all of the momenta vectors (mass x velocity) along each space component, then at a later time (after a collision, say) that all of the momenta along all of those axes will still be the same. That's also true for rotational (angular) momentum, though it's sometimes harder to grasp that one because depending on your choice of origin for a system, there doesn't actually need to be anything rotating to have angular momentum. But they are both conserved, and importantly, they are conserved independently.