Water is both a Bronsted-Lowry acid and base.
According to Bronsted-Lowry theory, an acid is a proton donor whilst a base is a proton acceptor.
Consider the ionisation of water below:
As you can see, one water molecule donates its proton to the other to become a base whilst the other molecule accepts a proton to become an acid.
Therefore, we say that water is amphiprotic, meaning that it acts as both a Bronsted-lowry acid and base.