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The Goliath is a unit from the Factory that can be produced with an Armory, largely useful for its powerful anti-air attack although it can attack both air and ground. It has high range and damage which improves when it attacks air and the air attack can be further upgraded to a range that meets or outdistances about all air-to-ground. Dispatching some Goliaths with your Terran push can be wise, for preventing drops on your Siege Tank push, or masses of these units can be used defensively against massed air units.
The Goliath's air attack is actually two simultaneous attacks, meaning a unit's armor should be counted twice. In addition, it is an explosive attack type, so it does 50% damage to small units, 75% damage to medium units, and 100% damage to large units meaning it is most efficient against heavier air units but it still can be used to great effect even against Mutalisk and Scourge, small units, as can be demonstrated by professional play.
Loosely it can be thought of as a double-Marine, with twice the damage, health, and cost (albiet with some in gas) and slightly improved range without upgrades. It also has similar move speed which means it can choose some ground fights but is outpaced by air.
Researched at the Machine Shop.
Goliaths are generally used in conjunction with Siege Tanks, and sometimes Vultures or Valkyries in mech or mech-bio TvZ variants. The Goliath's purpose is to help stifle the Mutalisks. While Goliaths are relatively immobile compared to the Marine and Medic combination, its superior range and damage compensates. Goliaths high rate of fire and high health make them fare very well against Zerglings. Also, they have vastly longer range than Mutalisks which allow them to micro to some extent. Hold position micro is useful against enemy Mutalisks while running away to use the Goliaths' superior range.
Goliath, Vulture, Siege Tank "balls" that are fully upgraded are notoriously hard to stop.
With the advent of the Fantasy Build, Goliaths became more and more common on the TvZ battlefield.
Goliaths are used to help stop early Wraith attacks and are very good against Vultures with Spider Mines due to their range and damage. Commonly, drops have a Goliath or two in them in order to shoot down Wraiths or even approaching Dropships.
Some Terrans may also choose to harass the opposing player's economy with Goliaths. Because four Goliaths fit inside a Dropship, Goliaths are fairly efficient at killing SCVs.
Being the premier Terran anti-air unit, Goliaths are seen at least in some numbers in virtually all TvPs where the Protoss decides to use air units, which is often at least for Observers. Goliaths are sometimes seen in small numbers during the mid-game to pick off Shuttles and Observers. When facing Arbiters on the field a handful of Goliaths are useful to snipe them or force them back. Against Carriers, Terrans will generally pump mass Goliaths as their long range and high damage are the best deterrent to Protoss air.