Briefly describe the mechanism by which explosive volcanic eruptions are thought to influence Earth's climate?

Well Volcanic erruptions are very violent and effect the immediate climate around it, it really depends on the sort of Volcano, normal volcanos like Mount St Helens effected its sourroundings by clogging up the atmosphere with ash, and Sulpher Dioxide which are both ejected from a volcano, a Super Volcano can cause a volcanic winter, in which the Sun's light is not allowed through the dust and ash in the atmosphere causing the surface temperture to go down dramatically, by about -20 degrees. but your main concern is the explosion if your around the Volcano which is from pressure build up and explodes.