Fleming's left hand rule (for motors) shows the direction of the thrust on a conductor carrying a current in a magnetic field.
The left hand is held with the thumb, first finger and second finger mutually at right angles, as shown in the diagram below.
The Thumb represents Thrust (or resulting Motion).
The First finger represents Field.
The Second finger represents Current (in the classical direction, from positive to negative).
There also exists Fleming's right hand rule (for generators). You can remember which rule to use by recalling that the letter "g" is in "right" and "generator".
This mnemonic is named after British engineer John Ambrose Fleming, who invented it.