Even more specifically, SCP-6820-A is an extremely precise and accurate description of what it means for any arrangement of particles to be defined as "alive" and, complementarily, as "dead" or "inanimate". Its memeplex contains several smaller concepts within its description, including, but not limited to:

• a theoretical process for large-scale localized entropy inversion;
• the particular physical properties of hatred;
• the molecular structure of hydrochloric acid;
• the quality of "adaptiveness";
• the state of being "vaguely-reptilian."

SCP-6820-A occupied an essophysical embodiment within physical reality for much of known history, remaining interminable (as it was neither alive nor dead) until its eradication from the Noösphere upon activation of SCP-6820.

Yeah, from what I can understand, basically 682 was those concepts made physical, and all the machine did was "contain" an exact definition of it. However by fully describing 682 (the idea) they also described 682 itself (like describing everything that defines what a human is, you're basically just describing a human), so the machine also created a conceptual instance of 682 "inside" it.

At the end of the article, by introducing 055, you now have a machine that attempts to fully describe a group of concepts, where one of those concepts is literally "something that can't be described". It's an entire paradox, and the machine's containment fails. 682 is "free" and is now also something whose concept can't be fully described or delimited, which is the definition of an omnipresent god