The law of definite composition states that every compound has a definite composition by mass. What does that mean?

The law of definite composition essentially states that a chemical compound always contains exactly the same proportion of elements by mass.

As an example, take water, H2O. In one mole you have 2 mole H and 1 mol O. By mass, you have 2 g H and 16 g O (total 18 g). The ratio by mass is 2:16 or 1:8 for H to O ratio.

In another way, H is about 11% and O is about 89% by mass. It doesn't matter how much water you have (1 g, 1000 g, 34 moles), this ratio will always be the same.