A neanderthal is someone who is rude and not very smart. If your brother interrupts your garden party by spraying your guests with a hose, you can call him a neanderthal.
When neanderthal is spelled with a lower-case n, it means a cretin or a dolt — a rough, mean, and slightly foolish person. If you spell it with a capital N, it means an extinct species of human being, and it's the root of the lower-case version. The word Neanderthal is German, named for the Neander Valley where human fossils have been found, and around 1926 neanderthal became popular British slang for a "big, brutish, stupid person."