A volcano is an opening (or rupture) in the Earth's surface or crust, which allows hot, molten rock, ash and gases to escape from deep below the surface. Volcanic activity involving the extrusion of rock tends to form mountains or features like mountains over a period of time.
If you had a geyser erupting in your back yard which was spewing out hot water as a result of a near by volcano then the resultant water damage would likely be covered under your home policy. The immediate damage to your lawn because of the geyser breaking through would not.
Movement of the earth is not an insured peril in your home owner's policy but volcanic ash, lava or gases are not excluded. Likely if you live near an active volcano this issue has been addressed and could be excluded from your policy. This is similar to people living on a flood plain are going to have limited coverage for sewer backup. They will install pumps and alarms and can sand bag but will often have to bear the cost of repairs during spring run off and heavy rains.
If you choose to live in an area where there are known hazards then there is limitations to what the insurance will cover. You will be required to take on at least part of the risk yourself with limitations of coverage or higher deductibles.
Volcano