As the defining characteristic of this creature is its single eye, for a long time it was taken for granted that cyclops—Greek κύκλωψ—was an old compound meaning ’round-eye’:
*kʷékʷl–h3ōkʷ-s = *kʷékʷlo– + *h3ōkʷ–
*kʷékʷlo– ‘circle, ring’ (cf. κύκλος; English wheel)
*h3ōkʷ– ‘face, eye’ (cf. ὄψομαι ‘see (fut.)’)
In more recent years another, perhaps better, etymology has sprung up, with the original meaning ‘cattle-thief’:
*pḱú–ḱlōp-s = *pḱu– + *ḱlōp–
*pḱu– ‘cattle’ (zero-grade of Indo-European *peḱu ‘cattle’; cf. Latin pecu, Old English feoh, German Vieh, Sanskrit paśu)
*ḱlōp– ‘thief’ (agent noun from *ḱlep- ‘steal’; cf. verbs κλέπτω < *ḱlep-yō, Gothic hlifan)
This option implies a simplification of an initial *pḱ- cluster to k-. For another initial cluster simplification like this, cf. Andrew Sihler’s proposed etymology of Homeric τρυφάλεια (a kind of helmet) as literally ‘with four (reading τρυ- as reflecting the combining zero-grade form *kʷtru- of *kʷetwór- ‘four’) phaloi (φάλος, a part of the helmet)’ (Sihler 1995 §389.4a).
Comparative Indo-European mythology is rife with monsters and enemies on a mission to steal livestock—to name just a few, Queen Medb plays this role in the Táin Bó Cúailnge, as does the monster Grendel in Beowulf, and Odysseus’s own men slaughter the Cattle of the Sun in the Odyssey (with this sin precipitating their demise). It seems likely that the myth of the cyclops evolved with a similar function.