When electricity was discovered, nobody knew how it worked and electrons were unknown. So the scientists just defined one of the poles as "positive" and said that the current is flowing from positive to negative. That still is the definition of an electrical current's flow direction. This is why you see the right hand rule applied in cases where they are talking about the direction of current flow.

However, later scientists discovered that in most (but not all) materials current is carried by negatively charged electrons, which travel from negative to positive. The electron flow is thus opposite to the current flow. This is why you hear some people talk about the left hand rule (they are talking about the flow of the electrons NOT the conventional direction of current flow).

KNOW THE DIFFERENCE BETWEEN THESE TWO. IF YOU ARE NOT SURE WHICH DIRECTION A TEACHER IS USING MAKE SURE YOU ASK THEM IF THEY ARE USING 'the true electron current flow direction' (i.e. the left hand rule would apply for induced magnetic fields) OR 'the conventional current flow direction' (i.e. the right hand rule would apply for induced magnetic fields)! I have seen many people who go into first year engineering who were not really told this in high school and they become confused .

Just a Sidenote: In some materials (e.g. electrolytic solutions) the current is carried by positive ions, which travel in the current's direction. And in semiconductors there can be currents of negative or positive carriers, depending on the doping.