When two elements combine to form two or more chemical compounds, then the masses of one of the elements which combine with a fixed mass of the other bear a simple ratio to one another. This law is called law of multiple proportions.
For example, carbon combines with oxygen to form two compounds which are carbon dioxide and carbon monoxide.
The masses of oxygen which combine with a fixed mass of carbon in carbon dioxide and carbon monoxide are $32$ and $16$. Therefore oxygen bear; $32: 16$ ratio of $2: 1$.
Example 2: Sulphur combines with oxygen to form sulphur trioxide and sulphur dioxide. The masses of oxygen which combine with a fixed mass of sulphur in $\mathrm{SO}_3$ and $\mathrm{SO}_2$ are $48$ and $32$ . Therefore oxygen bear a ratio of $48: 32$ or $3: 2$.