Vespene Gas was first discovered in the Koprulu sector. It is green of color (which can change when contaminated), found in geysers on multiple planets and has a high energy rating allowing it to be used by terrans as fuel for vehicles and energy reactors. Purity of the vespene is very important as it can become explosive if contaminated.
Vespene can also be used by other races. The zerg feed on raw vespene to drive their greatly accelerated metabolisms. On the other hand the protoss use vespene as a catalyst for their psi-driven machines.
Vespene gas is the Starcraft
series' secondary resource, the primary being the crystalline formations known as minerals
The most basic units and structures do not require any to be produced, but you will need it eventually as you climb the tech tree.
Advanced combat units (e.g. Seige Tank) will require some gas, but it will always be less than that of it's mineral cost. On the other hand the few "spellcaster" type units (e.g. High Templar) cost more gas than minerals.
Structures follow similar logic for cost with basic structures costing none and advanced ones costing varied ratios.
Researching upgrades always costs equal parts minerals and gas.
To acquire vespene gas you need to locate a vespene geyser and build your race's processing building atop it. Once finished your harvesting units can enter the building, where they will come out moments later carrying a container of refined gas (worth 8 units) back to the closest HQ. Only one gatherer at a time can be in the building. The maximum number of harvesters needed for efficient harvesting will usually be 3.
Geysers have a fixed amount of gas that can be acquired, but unlike minerals once this reserve is depleted you can still harvest from it at a reduced rate of 2 units per container in Starcraft and Broodwar. In Starcraft 2 on the other hand an exhausted geyser will produce nothing.