Breifly, a convection current is a current in a fluid that results from convection.
But, in more detail:
Convection is one of the three main types of heat transfer, the other two being conduction and radiation. Unlike the other two, convection can only happen in fluids,- liquids and gases. This is because the molecules have to be free to move.
Heat energy can transfer by convection when there is a significant difference in temperature between two parts of a fluid. When this temperature difference exists, hot fluids rise and cold fluids sink, and thencurrents (movements) are created in the fluid.