Cthulhu is a primordial entity associated with the Old Ones and the Elder Gods, who worships beings like Azathoth, the gibbering idiot star being at the center of the cosmos. Cthulhu is, more or less astronomically powerful, insane, possessed of sinister intelligence beyond mortal comprehension, psychic, and amorphous. It ranges in size from a buick to the Dubai Burj superscraper, and has been known to stand waste deep in the ocean and devour ships. It is a kind of interstellar alien entity with multidimensional attributes, and yet,
is nothing but a high priest to even more twisted, insane, non euclidean hyperdimensional entities representing the incarnations of the forces and aspects of the "other" part of human non understanding - the ineffable aspect.
The Cthulhu mythology was designed by HP lovecraft and inspired by Babylonian research conducted by classic cultists such as John Dee and the more recent Aleister Crowley, although they did not know each other personally. The most accurate portrayals of what Cthulhu means can be found in the following three films:
Cloverfield - a decent example of what Cthulhu would be like minus the interdimensional/sinister psychic aspect
Stephen Kings the Mist - solid representation of dimensional and psychological aspect, but on a smaller, less diabolical scale
Event Horizon - excellent representation of the sinister intelligence and psychic presence, but lacking in physical presence
Combine the three and understanding Cthulhu becomes a bit easier. Zalgo is an internet mem inspired by Cthulhu.