In short
The soul here refers to the spiritual side of being human—not just life as such, but the fact that a person who has died yet lives in the afterlife.
In Matthew 10:28 the soul is contrasted to the body, and as such the soul in this context must be referring to the spiritual component of being human. In this particular context soul cannot be referring to life as such, but rather the fact that a person who has died nonetheless continues to live in the afterlife. That this is the intended meaning here, is also evident from the verses that follow.1
28 And do not fear those who kill the body but cannot kill the soul. Rather fear him who can destroy both soul and body in hell.