Pure state is a quantum state that completely encodes the information about a quantum system. If the information about a quantum system leaks into the environment the state becomes “mixed”. Quantum computing relies on pure states which is why the environment is one of the major enemies of quantum computing.

Classical bits can be 0 or 1 which are usually encoded as voltages $0V$ and $5V$ respectively. These voltages are not precise. They can vary up and down due to thermal noise, electromagnetic interference, current leakage etc. However digital computers are remarkably resilent to erorrs.