With convection, hot mantle material rises closer to the Earth's surface, raising the geothermal gradient in the area. This causes the temperature in the earth's mantle to rise, which causes the mantle to partially melt. The partial melt contains both liquid and crystals that need a higher temperature to melt.
Partial melting is an important process in geology with respect to the chemical differentiation of crustal rocks. On the Earth, partial melting of the mantle at mid-ocean ridges produces oceanic crust, and partial melting of the mantle and oceanic crust at subduction zones creates continental crust.