Can someone explain divergent and convergent boundaries to me?
No, you have trenches wrong. They are associated with (some) convergent boundaries. Divergent boundaries are where crust is undergoing extension (due to upwelling magma). This mainly occurs at the mid-oceanic ridges and at some continental areas (like east Africa). Convergent boundaries are where crust is undergoing shortening. This is mainly occurring at continental margins where oceanic plate is being subducted (creating trenches), but also is occurring at continent-continent collisions and older oceanic plates subducting under newer oceanic plates. The Marianas Trench is the deepest trench in the Earth, and it is associated with one oceanic plate subducting another oceanic plate. Convergent boundaries commonly build mountain chains (like the Andes Mountains) and are associated with back arc vulcanism (like the Cascade Mountains).