From Latin 'inter' (among) + 'tenere' (to hold) — originally holding guests among pleasant things. Also: holding an idea in mind.
To provide amusement or enjoyment for someone; to receive and host guests; to give consideration to an idea or proposal.
From Old French 'entretenir' meaning 'to hold together, to maintain, to keep someone engaged,' from Latin 'inter' (among, between) and 'tenere' (to hold). The Old French form evolved from earlier 'entre-' (between, among) plus 'tenir' (to hold). The original English sense was 'to maintain' or 'to keep in a certain condition,' but by the sixteenth century the dominant meaning shifted to 'to keep someone engaged or amused' — holding their attention among pleasant things. Key roots: inter
The phrase 'to entertain an idea' preserves the oldest English sense of the word — not amusement but reception and consideration. When you entertain a thought, you are doing what a medieval host did with a guest: receiving it, holding it among your other concerns, giving it attention and hospitality. The intellectual sense and the hospitality sense are the same metaphor: welcoming something in and holding it for a time.