Plain English Meaning
When the airplane gets bumped around or moved sharply, the floating card inside the magnetic compass rocks back and forth and you can't get a steady heading off it. You have to wait for it to stop swinging before you can trust the reading.
Full Definition
A magnetic compass error caused by the compass card swinging or wobbling back and forth during turbulence or abrupt control movements, making it difficult to read an accurate heading until the card settles.
Context Anchor
Seen in instrument flying when learning the limits and errors of the magnetic compass.
Derivation
Oscillate' comes from the Latin oscillare, meaning 'to swing.' It originally described the swinging motion of a small hanging object. In the compass, the card itself is the thing swinging, which is exactly what makes the heading to read.