Starkiller Base is a planet-sized military installation with a superweapon capable of destroying multiple planets in a targeted star system from interstellar range. The beam it generates propagates at superluminal speed, reaching and destroying the target within minutes of the weapon's discharge.
Starkiller Base consumes an entire star to power its weapon, indicating that the beam carries the total potential energy that the star could generate over its remaining lifespan.
The base has a planetary shield to protect it from attack. With the shield operational, starships, energy beams, and projectiles can not reach the surface. The limits of the shield are not known, but the Resistance certainly has no resources capable of defeating it. It will not, however, prevent a ship from passing through while traveling in hyperspace (although that, itself, is a nigh-suicidal undertaking).
The energy needed for the weapon is more than sufficient to destroy the base, so active systems are required to keep it contained. One of these systems is a "thermal oscillator" housed in a facility on the base's surface. Destruction of this facility while the weapon is charged to fire will destabilize the containment system and destroy the base.
While it did not demonstrate any propulsion ability, given that it consumes a star to recharge the weapon and it is not a one-shot weapon, it is presumably capable of getting from one star system to another.