Why are functional groups important in biology?
Functional groups are what make molecules do what they do.
A functional group is a collection of atoms in a molecule that are responsible for the characteristic reactions of the compound.
A functional group is, if you like, what gives a molecule its 'character'. It defines the chemistry of the molecule in terms of what it can do.
For example, look at an amino acid. All amino acids have the same backbone:
But it is the functional group (the R in the above) that gives the individual amino acids their unique properties. In the image below you will see that the R has been replaced with a collection of other atoms to yield all the different amino acids.