When a volcano erupts, lava (we call magma "lava" once it is outside of the volcano), ash, and bits of rock from the top of the volcano get propelled into the air because of the extremely high force of the eruption. Volcanoes erupt because of the buildup of pressure inside of the volcano. This pressure buildup is because gases inside of the volcano (like water and carbon dioxide) expand, putting pressure on the rock which surrounds the magma chamber. Eventually, the buildup of pressure is so much that the rock surrounding the magma chamber cracks, letting the magma come up to the surface, and the volcano erupts.

A good "take home" experiment for how this works can be done in your backyard (with help, please do not do this without adult supervision!). You will need a bottle of Coke and a Mentos candy. If you put a Mentos candy inside of Coke, a chemical reaction occurs, and a TON of carbon dioxide gas is produced, causing the Coke to expand and "erupt".

Here's a YouTube video featuring this experiment as well: