The concept of current

As depicted in the diagram below, the current in a circuit can be determined if the quantity of charge Q passing through a cross section of a wire in a time t can be measured. The current is simply the ratio of the quantity of charge and time.

Thus, current as a rate quantity would be expressed mathematically as:

Conventional Current Direction
The particles that carry charge through wires in a circuit are mobile electrons.

Portrait of Benjamin Franklin

Benjamin Franklin, who conducted extensive scientific studies in both static and current electricity, envisioned positive charges as the carriers of charge. As such, an early convention for the direction of an electric current was established to be in the direction that positive charges would move. The convention has stuck and is still used today.

The direction of an electric current is by convention the direction in which a positive charge would move. Knowing that the actual charge carriers in wires are negatively charged electrons may make this convention seem a bit odd and outdated. Nonetheless, it is the convention that is used worldwide and one that a student of physics can easily become accustomed to. 

Source: http://www.physicsclassroom.com