means Completely preoccupied with someone or something, your thoughts circling back to it whether you want them to or not.

from From Latin obsidere, 'to sit down before, to besiege' — picture an army camped outside your city walls, refusing to leave. The past participle obsessus gave us the sense of being literally surrounded, hemmed in. Early English use was darker than ours: to be 'obsessed' meant to be haunted or beset by an evil spirit, a demon laying siege to the soul. Only later did the besieging force become a thought, a person, a hobby — the enemy at the gates now living rent-free in your head.