The Elder Things are extraversal alien entities native to a dimension known as Realms of Madness. While many dimensions and planes of existence are considered to be parts of our universe and merely 'layers' of it, these Realms and the creatures native to it are considered to be part of an entirely different universe which laws of physics have no relation to ours. These entities are extremely powerful and are responsible for the Titan Apocalypse which ended the entire Titan civilization in our galaxy and possibly all other galaxies as well.
There is no commonly agreed upon name for these entities. The most common one is Elder Things, which emphasizes their age (allegedly predating our universe) and their bestial nature. Other commonly used names are Old Gods, Elder Gods, Outer Gods, Gods of Madness or Star Gods, although some of these terms can at other times refer to unrelated entities.
It's unknown if the Elder Things have any philosophy that can be expressed with mortal languages, or any philosophy whatsoever, but their mortal worshipers posit a few claims. According to those Cults of Madness, the Elder Things are alien gods that are so incomprehensibly different from us that we cannot ever understand the very basics of their existence, not to speak of their own "beliefs". However, they claim that when the Titans opened the rifts to their dimension, they reacted violently and impulsively "as you would if your garbage spontaneously turned over and started to produce numberless counts of cockroaches". This suggests our universe is as alien to them as theirs is to us and the Titan Apocalypse was merely a single act of impulsive defense.
Followers of the Elder Things see their overwhelming power as a proof of them being the only true gods to have ever set foot in our universe. Because these gods seek to destroy all life in our universe in an act of disgust, the followers act, covertly or overtly, to further these goals and promote entropy in the universe through murder, wars and disruptive dark magic.
History of the Realms of Madness or the native entities is unknown prior to Titans opening the rifts to their dimension. Once that happened and initial scouting equipment was sent through and appeared to immediately disintegrate upon crossing over, the Titans attempted to close the rifts, unsuccessfully. Hordes of entities crossed over to our universe, although most of them failed to materialize properly and turned into motionless lumps of flesh or other seemingly random materials. The creatures that did materialize, however, were horrific abominations whose physical construction varied from unnerving, to disgusting, to mind-bending in ways it violated basic geometry.
The Titans eventually closed the rifts but not until numerous creatures were already in our universe and most of the Titan civilization was destroyed. The aberrations remained lurking in dark places of our universe since then, and the Elder Things made no explicit contact although their influence can corrupt minds of mortals to lose their grip on reality and embrace Cults of Madness that claim to worship the Elder Things as gods.