The Earth's crust has a dual personality. On one hand, there are the continents. Many times, the crust that makes up the continents can be very old, upwards of 3 to 4 billion years old! Yet, the oceanic crust that makes up a majority of the planet's surface doesn't get anywhere near as well. In fact, the oldest oceanic crust is only about 220 million years ago, or ~5% of the age of the Earth. We know we've had oceans and oceanic crust for billions of years, so where has it all gone?
That's where subduction comes in. Subduction is the process where pieces of the Earth's crust get literally shoved back into the next layer down (the mantle). The mantle isn't a rigid solid but rather a plastic solid, so it can deform as the crust gets pushed into it. It also isn't as dense as old crust, so that crust will "sink" through the mantle, maybe ending up at the boundary between the mantle and core thousands of miles below our feet.
