Empleko (ἐμπλέκω) means to weave into, entangle, or become involved in something — to be caught up in something that binds. It appears twice in the New Testament: 2 Timothy 2:4 instructs soldiers of Christ not to 'entangle [empleko] themselves in civilian affairs,' and 2 Peter 2:20 warns that those who have escaped the world's corruption but become 'entangled [empleko] in it again and are overcome' are worse off than before.
The military metaphor in 2 Timothy 2:4 is vivid: a soldier on campaign cannot let the affairs of ordinary civilian life wrap around him and pull him away from his commanding officer's orders. Paul applies this to Christian ministry — the focused, unencumbered devotion required of a gospel worker. The 2 Peter 2:20 use is more sobering: empleko describes the spiritual trap of re-entanglement with sin after experiencing salvation. The Greek word suggests threads woven together — the more you struggle against entanglement, the tighter it can hold. The solution is not self-effort but keeping one's eyes on the Commander.