How are functional groups related to reaction types?
Functional groups inherently define the types of reactions that can take place.
Experimentally, chemistry came up the other way and used observations of reactions to eventually figure out what atomic/molecular configurations caused or allowed them to occur. We call them “function groups” because they are the 'groupings' of atomic structure that create the 'functionality' of a particular reaction.
Thus, alcohols, ketones, aldehydes, acids, and all the other named functional groups tell us the likely reactions those molecules can have. This is a key part of organic chemistry synthesis and the understanding of complex biochemical systems.