How igneous and sedimentary rocks turn to metamorphic rocks?

Heat, pressure and chemistry compounds around the rocks.

Explanation:

Metamorphic rock is formed by pre-existent rocks (igneous and sedimentary, sometimes from another metamorphic rock), those rocks were modified by the effect of heat (high temperature), pressure (under the terrestrial surface) and chemistry compounds around the rocks. The physical and mineralogical composition becomes different than the original form.

This process is called metamorphism.