What is the functional group of an aldehyde?
An aldehyde is a functional group by definition. Other examples of functional groups are ketones, ethers, esters, amines, amides, carboxylic acids, acyl halides, etc. The term "functional group" just implies that it is likely the area of a molecule where a reaction will take place.
When looking at an aldehyde, it is characterized specifically by the presence of R-CHO, which looks like this when drawn out:
The part of the aldehyde that will react is the carbonyl, or C=O portion. Because the oxygen is more electronegative than the carbon, it will create a dipole in the bond, resulting in a partial positive charge on the carbon, and a partial negative charge on the oxygen.