Mar 9:44 Where their worm dies not, and the fire is not quenched.
Alternative: Where their worm never ends and the fire does not go out.
This is the first of three repetitions of this phrase at the end of this chapter. When Christ does three repetitions, his metaphors usually cover the three aspects of temporal life (physical, emotional, and intellectual, see here for more). In this case, the three symbols used in these series of repeating verses are the hand, foot, and eye, representing the emotional (our relationships with others), physical (our physical bodies), and intellectual (our mind).
The immediate context here describes our lives ending up on a trash heap. While Christianity teaches this is about the punishment of hell, looking at the context and Christ's words describing good and evil, sin, and forgiveness, it is much more about leading worthless lives. The idea of endless worm and the continued fire seems to be about being trapped in the awareness more like an animal instead of moving onto a spiritual awareness of real life.
The worm described here is specifically the worm that lives on dead bodies. The idea is that until we are reborn of the spirit, we are dead. In the previous verse, Christ describes cutting off our hand as getting rid of the physical aspects of our life, in this case, our relationships (specifically worrying about our place in society) that are holding us back. Our spiritual awakening is "entering into life."
As long as we don't do that, our pain continues and our "worm" never stops. These three repetitions of this line are Christ's only reference to the term "worm" but he actually alludes to it when he is dying on the Christ. The words "My God, my God, why have you forsaken me," are the first line of Psalm 22 (translated here), which also references us as worm because our social relations betray us: "I am a worm, not a man, scorned by humanity, despised by people." However, since the "worm" is repeated three times, however, it represents the betrayal of all aspect of our temporal existence: emotional, physical, and intellectual.
"Worm" is from skôlêx (skolex), which means "worm," specifically, "earthworm," "grub," "larvae," and "worms in dung, decaying matter and trees and word."
"Die" is from teleutaô (teleutao), which means "to bring to pass," "to accomplish," "to finish," "to die," "to end a life," and "to make an end to life." (Christ uses this word Mar 7:10, for the OT Hebew word, muwth, which means "to die" and "to kill.")
"Fire" is from pur (pyr), which means "fire," "sacrificial fire," "funeral fire," "hearth-fire," "lightning," "the light of torches," and "heat of fever."
"Quenched" is from sbennumi (sbennymi), which means "quench," "put out," "dry up," "run dry," and "go out."