First off, most countries use the Metric System, so if we're converting from Customary to Metric or vice versa, then it's important to know.
Also, if you're doing the measurement in things like baking, it's important to know the conversion units.
Example:
Let's say you need 1 cup of sugar, but you only have spoons that measure a teaspoon. You need to know the conversion so you don't put too little or too much sugar.
Hope this helps!