Fleming's Left Hand Rule is a useful way to remember the relationship between the current, a magnetic field and the force created. When current flows through a conducting wire which is inside an external magnetic field, the wire (and the external magnet) experience a force. The force on the wire is perpendicular both to the external field and to the direction of the current flow. In other words they are mutually perpendicular.

The reason that there is a force on the wire (and on the magnet in the opposite direction - that is action and reaction) is that the field of the permanent magnet and the magnetic field around the wire interfere with each other causing a force in the direction of the arrow.The force will be greater if the permanent magnet is stronger, if the current is greater and if there is a greater length of current carrying wire within the magnetic field. If the wire is not perpendicular to the field the force will be reduced.

A left hand can used, as shown in the diagram below,  to represent the three direction all at right angles to each other. Using the thumb, fore finger and middle finger, each finger is labelled with a quantity. Shown in the diagram below these are force, magnetic field and electric current (conventional flow not electron flow).