Rocks on the ocean floor are expelled from the molten mantle through Mid-Ocean Ridges, areas where the tectonic plates of the Earth are moving apart. This allows the liquid rock from underneath the plates to move upwards and cool as it hits the water. These rocks are younger than the rocks at a Subduction Zone, because there are closer to point of origination. At the subduction zone, one tectonic plate is pushing underneath another, recycling its material into the molten mantle; by definition, this plate has been moving away from the mid-ocean ridge since it was first formed. While the ocean floor moves and so rocks from far away may be pushed to new locations, generally speaking the rocks near a subduction zone will be older than those near a mid-ocean ridge. 

Is the ocean floor older at a Mid-Ocean Ridge or at a Subduction Zone?

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.