The idea behind memristors started as a theoretical prediction way back in 1971 and is considered to be the "missing link" in electronics, a fourth basic circuit element in chip engineering to supplement the more familiar resistor, capacitor and inductor that form the basis of every electronic device. In short, memristors are resistors with memory capabilities -- they change resistance when electric current is applied and can 'remember' off/on states without power. This makes them great candidates for storage devices that require little energy to function.
Memristors could potentially be used in logic circuits as well, replacing the billions of transistors inside today's microprocessors to handle computation more efficiently and occupying far less space. For now the HP and Hynix partnership is focused on storage technologies, though. Under the agreement, Hynix will implement HP's memristor technology in its research and development fabrication plant. Actual ReRAM products could ship in three years.