Tautomerism is a phenomenon of a change in position of an atom in the compound, leading to a change in the functional group and the number of single/double bonds. Tautomers are isomers i.e they have the same chemical formula, but different structures. In many cases, the tautomers of a compound coexist and are considered the same compound, though their structures are different. Protons are often the atoms that change position. 

Let us understand it with the help of the following example.

The most common type of tautomerism is the keto-enol tautomerism. As the name suggests, the keto compound (one with a carbonyl group) tautomerises into an enol compound (which contains an alcoholic group; note that the double bond in the carbonyl group disappears when it becomes an alcoholic group. The lost double band appears somewhere else in the compound as we will see, so that the overall unsaturation remains the same).

The below image illustrates the mechanism: