Plain English Meaning
The speed that keeps the airplane in the air the longest while gliding down, even though it won't travel as far as it could at a faster glide speed.
Full Definition
The airspeed at which an unpowered airplane loses altitude at the slowest possible rate, allowing it to remain airborne for the maximum amount of time. It is slower than the best glide airspeed, which gives the greatest distance covered per unit of altitude lost.
Context Anchor
Encountered when learning glide performance, especially when comparing staying airborne longer versus covering the greatest distance during an engine-out glide.
Derivation
"Sink" refers to the rate at which the airplane descends through the air. "Minimum sink" means the smallest possible descent rate -- so this is the speed that produces the slowest downward movement.