Tautomerism basicially means that you have different isomers that are able to convert into each-other. This is not really similar to hyperconjugation which is an electronic effect in a given molecular geometry. The main difference between them is that hyperconjugation is thought to be a property of a given molecular geometry while tautomerization is an equlibrium between separate, distinct, stable configurations.
There are many types of tautomerizations, as explained for example on the Wikipedia. Probably the most well-known type of tautomerisation is the keto-enol tautomerisation, which is an equilibrium between a ketone molecule and an enol (an alcohol connected to an $sp^2$ carbon). The equilibrium between two isomers is the explanation why enols are only stable under special scenarios: they tautomerise into ketons! Another important example for tautomerism is the equlibrium between the chain and the ring isomers for sugars.
So again: tautomerism is an equilibrium between different (real, existing) isomers as opposed to hyperconjugation which is just defined within a single structure.