A slat is an aerofoil attached to the leading edge of the wing. In most cases it can be moved forward to produce a convergent slot. Air flowing up through this slot is accelerated, causing the boundary layer on the upper surface of the wing to be energised. This delays boundary layer separation and so increases the stalling angle of the wing. In some cases the slats also move downards to act as leading edge flaps, increasing wing leading edge camber.
Krueger flaps are small panels fitted to the underside of the leading edge. They are hinged at the front and deploy downwards into the airflow. This increases the camber of the wing, which in turn increases CL. But in most cases the resulting shape is fairly crude. This decreases the stalling angle of the wing
By fitting kruegers inboard and slats outboard, it is possible to ensure that the wing root stalls before the tips. This effect is often the subject of JAR ATPL POF questions.