Charge is the state of being electrically active. It is caused by an imbalance in the numbers of protons and electrons that are present - more protons results in a positive charge, and more electrons results in a negative charge. Protons do not normally move around very much, so charge is mainly created and transferred via the movement of electrons. Electrons always tend to flow from areas of negative to positive charge; this flow is called electric current, or it can manifest itself as static electricity where charged objects physically move towards each other.
Charge is measured in Coulombs.