What are these river/canyon-like carvings in the ocean?
The carvings are submarine canyons, a part of the continental slope leading from the continental shelf to the continental rise and ultimately the Abyssal plains. They are a product of :


erosion through currents and 
slumping of the continental shelf


Like other erosive or slumping effects, they can be self-reinforcing, leading to canyon-like structures. The highlighted canyon here is the Gollum Channel system, seen here.