In horror circles the term has become commonplace. It’s our “Shakespearian”… only with much larger tentacles.
The term Lovecraftian comes from H.P. Lovecraft and is closely associated with the Cosmic horror subgenre. They are often used interchangeably, but for simplicity we’re using Lovecraftian as a major (probably the main) trope underneath Cosmic horror. Notable authors who dabbled with the themes associated with Lovecraft before Lovecraft include Edgar Allen Poe and Algernon Blackwood. And certainly there is a lot that has been done since. So one could argue both to be Lovecraftian and to exist as Cosmic horror is not wholly to be associated with H.P. Lovecraft.
There are many common elements of Lovecraftian storytelling, such as creatures appearing from alternative dimensions, cults, and of course the dreaded “old gods” such as Cthulhu.