It is analogous to a pile of wooden blocks. Suppose you dump a box of blocks onto the floor in a big pile. Now scatter the blocks so that no block is on top of another. There is still no long-range order, but the disorder is now very different. Many astrophysical sites experience low pressures, low temperatures, or both - ideal conditions for forming amorphous ice.
Comets are one example.
If comets are dominated by amorphous ice, it could have significant implications for cometary activity, such as the jets that comets squirt into space. As a result, energy is released. Thus, as a comet approaches the Sun, its ice may transform from amorphous to crystalline, generating energy. This energy further warms the ice and accelerates cometary activity. Amorphous ice may also be important in the interstellar medium where it coats dust grains in dense molecular clouds, the birthplaces of stars.