The simple answer of what happens at the boundaries of plates is that they are constantly moving and their movement defines them. There are three different types of plate boundaries: convergent, divergent and conservative plates. The divergent plates are constantly moving apart and magma flows up between them creating more ocean floor. Convergent plates overlap and the magma which rises stays beneath the plates to forms ridges. The conservative plates don't create or destroy ocean floors but just slide back and forth. The conservative plates are the cause of earthquakes such as we see in California.
plate boundaries are the sites of many geologic phenomena. What is made at each boundary depends on the movement and interaction of the plates.
In a divergent plate boundary, plates are moved apart from one another. This is happening at mid-ocean ridges like in the middle of the Atlantic Ocean. As plates rip apart, new crustal material cmoes to the surface due to the density of the liquid material. As it cools, new ocean floor material is made. This can also be found on land at rift zones like the East African Rift zones.
Convergent boundaries come together, but can illustrate 3 different formations depending upon their collision types. When 2 continents slam into each other, folded mountains occur like what is currently happening in the Himalaya mountian rain where Indian is slamming into Eurasia.
If 2 ocean plates smash into one another, an extremely deep trech can be formed like what is seen in the Marianna's trench.
Finally if a continent and ocean plate hit each other, a subduction zone is created. Ocean material being more dense is thrust under the continents into ocean trenches where the ocean floor eventually will melt into asthenopshere. The continents are deformed making volcanic ridges.
The last plate movement is a transform movement where plates slide next to one another. No plate material is made or destroed here, but is does form transform faults.