to remain: to keep on being where, what, or as one is, rather than leaving, ending, or changing
At its heart this is a plain word for continuing: someone or something keeps on, does not move off, does not run out, does not change. Greek used it for staying in a town, for a thing that lasts, for holding to a promise, and for the fixed stars that never wander. The New Testament writers take that ordinary idea of staying put and stretch it across an enormous range, from a traveler lodging overnight to God himself who never passes away.
The four shades below are one idea seen from different angles. To stay in a place, to last over time, to keep on in a situation, and to live in close union with another are not four separate words; they are the same continuing held against four backgrounds: place, time, condition, and relationship. The reason one word can do all of this is that each use answers the same question in a different key: what keeps on, and does not give way?
John and the letters of John make the relational shade the center of gravity. There the word names a mutual, lasting indwelling of Father, Son, Spirit, and believer that is at once a gift and a demand. But that deep use grows directly out of the everyday one: to abide in Christ is, in the end, to keep on with him and not leave, the way a guest stays in a house or a word stays true.