A first example of water's amphoteric character is the fact that it can self-ionize to a small extent. What that means is that a water molecule is capable of donating one of its protons (
Water can act as an acid or as a base in various chemical reactions, the most common two examples involving the ammonia and hydrochloric acid reactions.
Here water acts as a Bronsted-Lowry acid because it donates a proton to ammonia.
This time water acts a Bronsted-Lowry base because it accepts a proton from hydrochloric acid.
To be exact, in reactions that involve the transfer of protons, the term is actually amphiprotic.
Water can act as a Lewis acid or as a Lewis base as well; in such reactions, water can either accept a pair of electrons, which makes it a Lewis acid, or donate a pair of electrons, which makes it a Lewis base.
Here's another example of water's amphiprotic (amphoteric) nature: