According to the American Geophysical Union, lava forms in the Earth's mantle and flows to the surface through volcanoes. Internal gas pressure within the volcano causes it to spew lava with the amount of pressure depending on how much and how quickly.
Water, pressure and temperature are three factors that cause the formation of lava. The Earth's mantle is filled with crystals, and when these crystals get hot enough, they start to melt, creating lava.
Lava is brought to the Earth's surface because of several different reasons. In the case of the formation of the Hawaiian islands, lava came to the surface because there was a swell of heat deep in the Earth's layers. Other times, it is because of changes to the continental crust, specifically if it is brought to the same level as the hot mantle.