At a mid-ocean ridge, the sea-floor is growing in size because material from the molten interior is added to the total sea-floor size; this occurs as tectonic plates move away from each other. At a subduction zone, the sea-floor is shrinking because the tectonic plate is pushing underneath another plate, recycling its material into the molten interior; this occurs as tectonic plates move towards each other. Because of this, the sea-floor is younger at a mid-ocean ridge; this material is expelled from the molten interior and solidifies in the colder water above. The sea-floor is older at a subduction zone, as that material has been moving away from its origin location ever since it became solid.
To simplify, sea-floor material is "birthed" at a mid-ocean ridge, becoming part of the sea-floor mass that moves towards a subduction zone, where it is recycled into the molten interior. This makes mid-ocean ridge sea-floor younger than subduction zone sea-floor.