Flow of charge is known as current.This charge can be negative or positive. Theoretically current can be a flow of electrons or protons.In practicality due to ionic bonds in the crystal flow of protons will result in vaporising the conductor due to energy required to free protons.Hence in most practical cases current is taken as the flow of electrons.
By convention current is taken as flow of charge from positive to negative.Since protons are stationary only electrons movement is possible from negative to positive.By adhering to the convention we assume electron movement to be opposite in direction to movement of current.