The Brønsted-Lowry definition of acids and bases addresses this problem. In this theory an acid is a substance that can release a proton (like in the Arrhenius theory) and a base is a substance that can accept a proton.
An example of a proton acceptor is ammonia (NH3). The ammonia is happy to accept a proton from the hydrogen of water (H2O) to become NH4. NH3 + H2O = NH4+ + OH-.
So NH3 is a Bronsted lowey base.