The basionym is the first name ever given to a taxon. Further studies and revisions may reject the basionym as the most correct one, but it still is useful as a nomenclatural refference for that species.
A short example: Linnaeus classified the Tea Plant as Thea sinensis. Some decades later, Sweet noticed that the genus Thea wasn´t really different from the genus Camellia, and renamed all the Theas as Camellias. Thea sinensis became Camellia sinensis, because he had to keep the specific epithet the same as the original name (basionym) for that species, given by Linnaeus.