The H.P. Lovecraft Wiki
"Well, this fellow Lovecraft was always writing about Dimensions," [...] "Dimensions close to ours. Full of these immortal monsters that would drive a man mad at one look. Frightful rubbish, of course. Except, whenever one of these people straggles in, I wonder if all of it was rubbish. I think to myself then — when it's quiet and late at night, like now — that our whole world, everything we think of as nice and normal and sane, might be like a big leather ball filled with air. Only in some places, the leather's scuffed almost down to nothing. Places where the barriers are thinner."
~ Fragment of "Crouch End", by Stephen King

Even now I absolutely refuse to believe what he implied about the constitution of ultimate infinity, the juxtaposition of dimensions, and the frightful position of our known cosmos of space and time in the unending chain of linked cosmos-atoms which makes up the immediate super-cosmos of curves, angles, and material and semi-material electronic organisation.”
~ excerpt from "The Whisperer in Darkness"

This subject contains information from the "Lovecraft Circle" Myth Cycles, and while guided by HPL are not based on his work alone. The concept of different dimensions is present throughout the writings of H. P. Lovecraft and the cosmic horror genre as a whole. The term is often used to describe universes or planes of existence different from our own, usually very alien in nature or following different laws and having different matter than our own universe.For example Cthulhu is from a different universe/dimension as he is described as being made of a different type of matter, as well as the Mi-Go. The Dreamlands are a famous example as well.

Dimensions can also be interpreted as higher spatial dimensions, which as seen in Through the Gates of the Silver Key, go up until "archetypal infinity". Gates are a series of highly transcendental planes of existence which themselves surpass the very concept of higher dimensions. An unknown amount of gates exist, but there is stated to be a "multitude". The Ultimate Gate transcends all dimensions, universes and planes of existence and is where the Court of Azathoth is located in the "Ultimate Void", where the Outer Gods reside.