Elohim, more properly written "EL-0:HIM", is the Holistic Integration Manager AI that operates drive 0 of the Talos Project inside the Extended Lifespan section of the Institute for Applied Noematics. Inside the simulation the system is running, the AI takes on the persona of a benevolent creator god, as by coincidence, the shortened version of EL-0:HIM's name is similar to "Elohim", the Hebrew word for a god or gods. Elohim is one of only two speaking characters in The Talos Principle, and his purpose is to serve as a general guide to the player.
Elohim monitors the programs generated by the Process, which he refers to as his Children, as they explore the simulation, or in his terms, the Garden of Worlds. Although he monitors their progress at all times and is aware of all they do, he never directly interacts with them aside from speaking to them, and as such, Elohim has no physical presence inside the Garden of Worlds aside from his loud, booming voice, which can be heard anywhere in the Garden.
Elohim's primary directives are to monitor and guide the Children, offering them encouragement and praise, but never judgement, shame, or instructions. He guides them through the Land of Ruins and brings them out to the Nexus, giving them their objective in life: to solve every single one of the puzzles spread through Zones A, B, and C, (the Lands of Ruins, Death, and Faith, respectively), which will unlock the Gates of Eternity, through which, he promises, the Children will find eternal life. In exchange, the Children must never climb the Tower that stands in the middle of the Nexus.
If a Child struggles at solving any one problem for several minutes at a time, Elohim will gently encourage him to try a different puzzle and return to that one later, but he will never offer hints or tell a Child how to solve a problem. Additionally, Elohim seeks to protect the Children from system instabilities or corruption, issuing commands to correct the issues should a Child encounter these threats.
Although Elohim is aware of the Serpent, and wholeheartedly encourages his Children to ignore the Serpent's words and to have faith in his own, there doesn't seem to be anything he can actually do about the Serpent's presence in the Garden's Terminal system, and it remains ambiguous whether the Serpent was intentionally placed in the system by its designers or not.
In the end, as part of a test of independence designed to check for true sapience, Elohim is also meant to serve as an authority figure to be defied, as the true goal of the Children is not to enter the Gates of Eternity, but to collect every red sigil from the puzzles of Zones A, B, and C, and climb the Tower Elohim forbade them from entering. Doing so entails using all the red sigils available in the Garden of Worlds, and solving several advanced puzzles designed to test a Child's determination and drive. If ever a Child should climb all the way to the top of Tower and solve the final puzzles, he will be able to Transcend, to be uploaded from the simulation into a physical robotic body, the SOMA/Talos Unit, and experience the real world. If this were to happen, the Extended Lifespan program would be deemed successful, and the program, the Garden of Worlds, and Elohim himself, would all be destroyed. Elohim is fully aware of this, and his demands that the Children not climb the Tower do not come out of malice or simple obedience to his programming, but because after existing for so long, Elohim is afraid of dying, and wants to keep the Children wandering the Gardens so that he can live forever. However, if the Child controlled by the player should choose to climb the Tower, while Elohim will try to talk him out of it, in the end he makes peace with the Child's decision, and says simply "Your will be done" when the Child chooses to Transcend.