heathfield is correct with the definition of amphoteric.
The word is used to describe a chemical compound that may behave either as an acid or a base depending on the environment. As examples, zinc oxides and hydroxides behave as acids in alkaline solutions and bases in acidic solutions.
Amino acids are amphoteric organic acids that contain the amine group, -NH2 and the carboxylic acid group -COOH. Amine groups are basic ( you could say they are a modified form of the ammonia molecule) and carboxylic acid groups are, let's see, acid.
As an example of the amphoteric nature of an amino acid, we can look at Glycine, which is chemically, the simplest of the amino acids.
Glycine has the formula H2NCH2COOH (C2H5NO2). In this case, Glycine has the amine group -NH2 (H2N) that is basic in nature on one section of the molecule, and the carboxylate group( -COOH) that is acidic in nature on another section. Both these groups are attached to the same carbon atom.
I'll leave a discussion on the interaction of the groups and Zwitterions in solution for another day.