Starkiller Base is a superweapon built into the planet Ilum by the First Order. Like the Death Star I and II, Starkiller Base was capable of destroying entire planets. However, it was superior to the previous models. It relied on energy harvested from the sun (which they absorb into the planet's core), was several times larger than the Death Stars, and could destroy more than one planet at a time, its first target being the Hosnian system, the seat of the New Republic's Senate.
Starkiller Base was destroyed thanks to the efforts of Han Solo, Finn, Rey, and the Resistance X-Wing Fleet, but at the cost of Han's life and half of the fleet's lives.
Starkiller was the last name George Lucas had originally intended to use for Luke and Leia before changing their last name to Skywalker.
The name "Starkiller" has also been used for various subjects in the Star Wars universe, including the (Legends) secret apprentice of Darth Vader in The Force Unleashed series of video games aka Galen Marek.
It is heavily implied in the game Jedi: Fallen Order that the planet Ilum, where the Jedi find the kyber crystals that power their lightsabers, was hollowed out and converted into Starkiller Base. This was later explicitly confirmed in supplementary material for The Rise of Skywalker.
Starkiller Base preparing to fire.
Starkiller Base firing its planet-shattering beam.
Starkiller Base absorbing the sun.
The energy of the Sun being absorbed into the Ilum's core
Hologram of Starkiller Base's size compared to the original Death Star.