Gauss Cannon is the green attacker unit from the base set. Its gold cost is high for only 1 attack, however its 5 Fragile health make it worth it to go against breaches. It is also the only unit from the base set that cannot be targeted by Apollo, as long as it has more than 3 health.
Gauss Cannon is a bit expensive for only one constant attack (Tarsier provides only one less damage over the course of a game for a far lower cost), so it should usually not be your main source of damage, but it can be your best option when you already have and don't need it for defense.
Gauss Cannons are especially useful when the game whittles down into the late-game and breach is imminent, or when going for a Breach me I don't care strategy; they will survive longer than most other attackers thanks to their high health. Beware that low health attackers, like Tarsier and Shadowfang, do not pair well with Gauss Cannon, as in a breach situation your opponent will focus your low health attackers. Thus Gauss Cannon are better paired with other high health units like Iso Kronus.
Gauss Cannons are also constructed by the Gauss Fabricator, which builds one Gauss Cannon per turn for eight turns.