Why is an alkylamine more basic than ammonia?

Alkyl Amine is more basic than ammonia because of the +I effect of the Alkyl group present. It donates its electron cloud to the nitrogen group therefore nitrogen has a greater tendency to donate it lone pair of electrons. This makes it more basic than ammonia where such a positive inductive effect is absent.

There is a concept in organic chemistry known as the inductive effect. Within the context of your question, the inductive effect means that attaching carbon chains to an amine will raise the energy of the lone pair on the nitrogen, because carbon (in the alkylamine) will withdraw less electron density from an atom of interest than hydrogen (in ammonia). That explains why alkylamines are stronger bases than ammonia – the alkylamine has a greater gain in stability when protonated than ammonia does, which makes it a stronger base.