Amphoterism refers to a property to act as acids n bases...n molecules of amino acids contains both acidic n basic groups...hence it shows amphoteric behavior....
 Let's start by defining amphoteric: 
"A substance which has characteristics of an acid and a base. It is capable of reacting chemically either as an acid or a base" 

This 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 apologize for the deep chemical explanations, I truly believe they will aid in the emphasis of this idea. 

Hope I helped!