A MNC is a corporation that does business (producing and/or selling) in more than one country. There are many important MNCs today and they are, some believe, growing in power. Since your other questions today have dealt with international relations, I will discuss MNCs' importance in IR.
To some IR theorists, MNCs are diminishing the power of states. They argue that the MNCs are coming to have more power than states, especially small ones. For example, if Chinese companies come to dominate the economy of Vietnam, those companies will be able to significantly affect what the Vietnamese government can do. If the Vietnamese government wants to change its economic policies, for example, it will have to be sure that its actions will not cause these Chinese companies to leave the country. In that way, the MNC has power over the actions of the governments of some countries.
If this happens, states become less important and MNCs have more power.