This site has a wealth of detail about how craters are formed.
For larger transient craters the modifications may take on a dramatic scale. Elastic rebound and collapse cause the excavation trajectories to go into reverse in a way, and the rock masses tend to move upwards and centripetally thus, accompanied by large-scale downfaulting, largely backfilling the transient crater. This will result in the formation of central uplifts and ring systems, and we may now refer to these as central-uplift or central-peak craters, peak-ring craters or multi-ring craters establishing the group of so-called complex impact craters or complex impact structures
Translated into simple terms, when the impactor hits the surface, some of the underlying rock is vaporized, while some of it is melted. This is called the contact and compression phase of the impact.
This molten rock will then be blasted away from the center of the impact. This is called the excavation stage. With smaller impactors, a bowl shaped crater is formed because almost all of the molten rock is ejected from the crater.
If the impactor is large, the excavation is deeper, and the crater will have a larger diameter. The molten rock will hit the outside edge of the crater and rebound, like ripples in a bathtub, towards the center of the impact. When these reflections coalesce in the center, they will create what are called central-uplifts.
Because molten rock is in a liquid-like state, it can 'splash up', creating the central-uplifts in the center of the crater. The image below of the lunar crater Tycho (85 km in diameter) shows such a central uplift.