The word "epitaxy" comes from the Greek and means: "to arrange on something". So, in epitaxy, atoms are arranged on a substrate (on its surface), which has a crystal structure. Atoms placed on the substrate arrange themselves according to the crystal structure of the substrate.
In homoepitaxy, the atomic layer consists of the same atoms as the substrate.
In heteroepitaxy, the atomic layer consists of different atoms than the substrate.
This is how semiconductor layers are created that are used in LEDs and lasers, for example.