An aspect is a portion of a god's power given physical form. Specifically, one particular aspect of their deific portfolio is transferred. This creature is alive in it's own right, and they often have a unique personality that is distinct from the god that spawned it.
By nature, gods are miserly regarding the expenditure of their power, and will always use as little of it as possible. If the task the deity is attempting involves battle, a god need only send the warrior aspect of themselves. By sending only the aspects of themselves that the job requires, they conserves power.
Slaying a god's aspect can seriously weaken that god and demote their rank in the Pantheon. The slayer of that aspect will typically absorb it into their own portfolio and take over that domain. The god who created the aspect will lose that part of their portfolio if that aspect is slain.
This is usually the only method available to mortals who wish to become gods, but do not have a patron deity to willingly promote them.