Hückel's rule
Furan is aromatic because one of the lone pairs of electrons on the oxygen atom is delocalized into the ring, creating a 4"n" + 2 aromatic system (see Hückel's rule) similar to benzene. Because of the aromaticity, the molecule is flat and lacks discrete double bonds. The other lone pair of electrons of the oxygen atom extends in the plane of the flat ring system. The sp2 hybridization is to allow one of the lone pairs of oxygen to reside in a p orbital and thus allow it to interact within the π system.