The connection between the plate boundaries and the volcanoes lies in that that they are both part of the geological activity on the planet, and that they are both found on roughly the same places.
On the places where there's plate boundaries, apart from the continental-continental convergent plate boundaries, there's a lot of geological activity. There's cracks that form through the crust, extremely high pressures, adjustments of rocks inside the crust, opining gaps between two plates. That leads to suitable conditions for the high pressure of the mantle layer to be able to push upwards the magma through this places. The magma is very hot, and supported by the high pressure from bellow, it manages to reach the surface relatively easily. Once the magma reaches the surface, it starts to lift up the surrounding area, forming a cone shaped feature, and once the crust is not able to stretch anymore, the magma breaks through it and in the form of lava comes on the surface, forming new crust. If we take a map where the volcanoes and the plate boundaries are marked, we can easily see that their locations correspond, expect for the volcanoes on Hawaii which are formed because of a hot spot.
