Decompression melting is an adiabatic process, that is, it takes place without any change in temperature of the region. Earth's crust is divided into a number of tectonic plates, which are constantly moving over the layer called mantle. This mantle is hundred's of kilometers thick and is actually solid, but behaves plastically. We constantly have a flow of hot mantle towards the earth's surface, only the temperatures are not high enough for melting to take place. At the regions of divergent plate boundaries, such as mid-ocean ridges, the hot mantle material rises up adiabatically and this causes a decompression or reduction in pressure. This adiabatic decompression results in reduction in melting point of the rocks and we end up with basalt magma.
Hope this helps.