What is current?

I am assuming that your question refers to electric current.
Electric current is motion of electric charges. The electric charges can move when placed in an electric field. That is, in the region of space where there will be electric force acting on the charges.
Electric charges that are free to move, if placed in an electric field, are found in certain materials called conductors. A metal wire is an example of a conductor. A conductor is used to connect an element where current is needed (such as a light bulb) to a battery, a device that produces potential difference (commonly known as voltage, a measure of change of electric field) between its two terminals. Together, a light bulb, a conductor and a battery can be made into the simplest electrical circuit. The flow of the electric charge around the circuit is electric current.
Electric current is measured as the amount of charge that flows through the cross section of a conductor in a unit of time:
I = (Delta q)/(Delta t) . The unit of measurement of the current is Amperes, after the scientist who discovered that the current-carrying wires create magnetic field.