Refer to figures.
Slats are aerodynamic surfaces on the leading edge of the wings. When deployed, the slat forms a slot which allows passage of air from the high pressure region below the wing to the low pressure region above it. Additional Kinetic Energy is added to the airflow through the slot by the slat forming a convergent duct.

When slats are deployed the boundary layer is re-energised. If Kinetic Energy is added to the boundary layer, boundary layer separation will be delayed to a much higher angle of attack.

In terms of the pressure distribution of the aerofoil with a slat extended, the slat provides a fair amount of lift itself due to its shape, and when extended, it flattens the peak of the low pressure zone somewhat, allowing the low pressure zone to be more evenly distributed over the top of the aerofoil. It increases the suction overall as it allows a much higher critical AoA and higher C_LMAX, as the adverse pressure gradient occurs more gradually, delaying the stall.

Furthermore, the suction peak flattens, it does not move. This is why the C_L location does not change very much when extending flaps.