Current is the amount of electrical charge flowing through an object, or through an electric circuit, at a given moment. While moving charge is normally carried by electrons, positive current is measured in the opposite direction from the flow of electrons, since electrons have a negative charge.
Different objects have different resistance. An object with high resistance, called an insulator, will have a lower current flowing through it. An object with low resistance, called a conductor, will have a higher current flowing through it.
The word "current" appears in the phrases "direct current" (DC) and "alternating Current" (AC) though those phrases don't specifically refer to current, and could more commonly be considered to refer to voltage.