Plain English Meaning
Keep the aircraft at the height you were told to fly at, and don't let it drift up or down.
Full Definition
To hold the aircraft at an assigned or selected altitude within acceptable tolerances, making continuous small adjustments to pitch and power as needed to prevent climbing or descending away from that altitude.
Context Anchor
Used during flight instruction, air traffic control instructions, maneuver practice, and any situation where the pilot is expected to hold a selected height.
Derivation
Maintain' comes from Old French maintenir, meaning 'to hold in the hand,' from Latin manu tenere. In aviation it carries that same sense: actively hold the altitude — it doesn't there on its own.