"Abide" has a number of definitions and senses and is used in a number of different ways in the scriptures. In the senses we will write about today, abide means to remain or to stay without going away; to stay habitually in a place; to remain in residence, to reside, to dwell. It can also mean to continue or persist in some state or action; to continue in existence, endure, to stand firm or sure, to remain steadfast. In a slightly different sense, abide can mean to await submissively or patiently (Oxford English Dictionary).
The root of the word abide means to trust or persuade. In that sense, abide means to await trustingly (The Roots of English). Some other words that come from the same root are faith, affidavit, confide and fidelity.