Each year as much as 150,000 tons of plastic debris, most notably styrofoam, washes up on the shores of Japan.
What does washes up mean?
This is a tricky phrasal verb, because it has at least three meanings:
You can find those meanings (or ones fairly close to that) listed here.
Based on your context, it's the second meaning. The styrofoam is left strewn about on the beach.
See Definition 19 on dictionary.reference.com. It means that the ocean carries the debris to the shore, where it gets stuck.