How is it possible for rocks to be trapped within another type of rock?
There are three major types of geological formations that contain or are composed of various rocks:

breccia
conglomerate
xenoliths

Breccia
The word breccia comes from the Italian word for rubble. There are various forms of breccia:

sedimentary
tectonic
igneous
impact
hydrothermal

The clast (rock fragments) within breccia are angular in shape and generally randomly orientated, a opposed to a conglomerate which is composed of rounded fragments.
Sedimentary beccia generally formed in ancient stream beds. Igneous breccia forms as a result of rocks being torn away during volcanic eruptions. Impact beccia results from the impact of meteorites. Hydrothermal breccia results from fissure opening up due to seismic or volcanic activity &amp; hydrothermal fluids (hot water) entering the fissure causing the sides of the fissure to collapse inwards.
Conglomerate
Conglomerates contain rounded rocks bound within a sedimentary unit. They form either within ancient stream systems or in marine environments. They can also form as a result of glacial activity.
Xenolith
Xenoliths are fragments of rock contained with igneous rocks. Their spacing with the host rock is much greater than that of beccia or conglomerate - they are more isolated. They generally result from volcanic eruptions.