Jake
There's the textbook definition: whenever the same two elements form more than one compound, the different masses of one element that combine with the same mass of the other element are in the ratio of small whole numbers. Which isn't all that helpful. Examples can add to your understanding of the definition.
Take carbon monoxide (CO) and carbon dioxide (CO2 ) as the example. A rough Interpretation of the law is that there is twice as much oxygen in carbon dioxide compared to carbon monoxide. Which, to us seems obvious because we know the formulas, but this law is what actually led to the discovery of chemical formulas. If we add numbers to this simple example we find that there are 16 grams of oxygen in CO and 32 grams of oxygen in CO2. Those numbers are the atomic mass values from the periodic table.