What does it mean to say the mass is conserved during a physical change?

Mater doesn't just appear or disappeared. Chemical elements are still there just the connections and how it combines changes.

So what goes into your chemical eqation must still exist after the change.

The total mass of the substance remains the same from beginning to end. The physical properties of the substance, such as size and shape, may change. The amount of matter in the substance does not change.