As lava flows from volcanoes and volcanic fissures, it cools and becomes what is called igneous rock. A "lava rock" is a more colloquial term that technically means any rock formed from cooled and hardened lava. It can also refer to a specific type meant for gardens and barbecues.
Igneous rocks include pumice, obsidian and basalt. The differences in these rocks come from what was happening when they cooled -- obsidian is from a fast-cooling, finely grained lava, for example -- and from the composition of the specific lava forming the rock. The Digital Atlas of Idaho notes lava containing feldspar and augite forms gabbro, while a combination of mica, hornblende, feldspar and quartz will harden into granite.
"Lava rock" also denotes a type of vesicular basalt, an igneous rock that has a smooth outer surface covering an interior riddled with hollows from gas bubbles. The rocks are used as inorganic mulches and in barbecues to help with heat distribution.