Because functional groups determine chemical properties of compounds.
Let's start with the defenition of functional groups. So, a functional group is a group of atoms that determine chemical properties of a compound.
And why is it important?
Well, if you take a molecule, does not matter how large it is, based on the functional groups present in the molecule, you can predict how it will react .
Here is an every day example: consider scissors and a long averruncator. Scissors are small and short.
Averruncator is large and long. But despite these size differences they function in the same way: they cut. This is because they have a common functional group : sharp blades
So, instead of memorisation of chemical properties for every single molecule, you can look at its fubctional groups and predict the chemistry of the molecule. And this makes chemistry really, really cool ;)