Functional isomers are structural isomers which have different functional groups, resulting in significantly different chemical and physical properties.
An example is the pair propanal HC–CH–C(=O)-H and acetone HC–C(=O)–CH: the first has a –C(=O)H functional group, which makes it an aldehyde, whereas the second has a C–C(=O)–C group, that makes it a ketone.
Another example is the pair ethanol HC–CH–OH (an alcohol) and dimethyl ether HC–O–CHH (an ether). In contrast, 1-propanol and 2-propanol are structural isomers, but  not functional isomers, since they have the same significant functional group (the hydroxyl –OH) and are both alcohols.
Besides the different chemistry, functional isomers typically have very different infrared spectra.  The infrared spectrum is largely determined by the vibration modes of the molecule, and functional groups like hydroxyl and esters have very different vibration modes. Thus 1-propanol and 2-propanol have relatively similar infrared spectra because of the hydroxyl group, which are fairly different from that of methyl ethyl ether.