The purpose of pre-pressurization is to avoid discomfort for passengers and crews during takeoff and landing.
By storing air in the cabin before the aircraft rotation or landing, the pressurization controller is able to smooth out:
The variations of bleed air supply when the engines deliver the highest thrust and need all available air.
The variations in both air supply and air release, due to the aircraft leaving or entering the ground effect. In particular this ground effect would force air into the cabin through the forward outflow valve when the angle of attack is increased for takeoff rotation or landing flare out.
However pre-pressurization involves relatively limited pressure differentials.
- 236 ft for a B737-NG (9 hPa).
- 140 ft for a Dash8-200-300 (5 hPa).
The case you mention seems ways higher with 40 hPa.
The source of cabin air for the aircraft is commonly bleed air from the engine compressor stages. Air is sent to packs for conditioning and enters the cabin (see a more complete description in this answer):
Bleed air pumped into the cabin then escapes it by one or two configurable exits, the outflow valves:
Outflow valve (and near to it the safety valve) on a Boeing 737-NG. Source
Cabin pressure is obtained by controlling the rates the air enters and leaves the cabin. This is indeed the job of the pressurization controller. This job is more difficult at takeoff and landing:
Air taken from the compressor is not used for the production of thrust, which can be a problem when thrust is critically required, e.g. for takeoff roll and rotation, or go-around. For these sequences, bleed air may be not available, or may be delivered at reduced or unstable rates. Normal bleed air delivery capability is restored after takeoff when the engines need less air.
The ambient pressure around the aircraft is subject to variations when the aircraft rotates and leaves the benefit of the ground effect, and also when it enters this effect before the flare. So the differential pressure at the outflow valve varies as well as the bleed air supply, and both need to be compensated too.
Unmanaged variation of bleed air supply or cabin air outflow create air bumps in the cabin. To avoid discomfort, on some aircraft the cabin is pre-pressurized at a pressure slightly higher than the ground ambient pressure.
The pre-pressurization occurs during the takeoff roll and shortly before landing. It creates a stock of air the pressurization controller can use to smooth out bleed air bumps.
Source: B737-800 FCOM:
The air/ground safety sensor signals whether the airplane is on the
ground or in the air. On the ground and at lower power settings, the
cabin is depressurized by driving the outflow valve to the full open
The cabin begins to pressurize on the ground at higher power settings.
The controller modulates the outflow valve toward close, slightly
pressurizing the cabin. This ground pressurization of the cabin makes
the transition to pressurized flight more gradual for the passengers
and crew, and also gives the system better response to ground effect
pressure changes during takeoff.
This additional amount of pressure mustn't compromise the ability to quickly open the doors in case of emergency, so pressure differential is limited. On a B737-NG, the differential is 0.125 PSI (9 hPa). This is equivalent to an altitude 236 ft below the runway. The system has a fail-safe mode which automatically opens the outflow valves quickly after the aircraft has landed (unless the Ditching switch has been pressed).
After the aircraft is airborne, or has landed, the pressurization system releases air previously stocked, to recreate a smooth altitude increase.
For the sake of completeness: The cabin will not "climb" or "descend" as fast as the aircraft, and will have its ceiling at 8,000 ft to maintain oxygen pressure at a safe level to breath without a mask.
Cabin pressure vs. atmosphere pressure
Here is a representation of the pressure differential during a flight (with the takeoff/landing highlighted. Note the cabin (dashed line) "is lower" than the aircraft.