Electrons are a stable sub atomic particle that has a negative charge and is found in all atoms and is the main carrier of electricity through solids.
In a metal, some of the electrons can escape from the atoms and are free to move around inside the metal. These electrons are referred to as 'conduction electrons'.
A current is a flow of charge. In metal a current is the flow of the conduction electrons through the metal. This can occur when connected to battery for example: The battery pumps the conduction electrons around the circuit.