As a space probe enters the gravitational field of the planet, some of the momentum of the planet is transferred to the momentum of the space probe. p=mv, as momentum of the planet is lost, it's velocity also decreases however the planet's mass is great enough that there is no significant change in velocity. However since the mass of the space probe is smaller, it experiences a significant increase in velocity (an acceleration).
Probably isn't the best way to get full marks on that question, but I hope it was somewhat helpful.
As the space probe passes by the planet, the planet's gravitational field draws the probe towards it and 'swings' it around at a faster speed, due to the slingshot effect. Here, due the conservation of angular momentum, the momentum of the planet is transferred to the space probe, which increases the probe's speed and direction.
Note: Since the planet has such a great mass, there is no noticeable change in its velocity due to this decrease of momentum (p=mv).