The Secret Society is an organized group of super-villains with the intent of taking down the Justice League. The original goal as visualized by Gorilla Grodd was to counter the League's round-table system and capitalize on their building interpersonal issues (which led to hampered teamwork) by pitting them against a well-organized team-built group of villains, something both versions of the Injustice Gang (JLU) were not. Eventually the league still won over them.
Later on, Lex Luthor found himself broken out of prison and was introduced by Grodd to a large conglomerate of villains, building on his original idea of an organized villains-united setup as well as guaranteeing side-by-side protection from the Justice League in many operations for a fee. Luthor eventually overthrew Grodd when he learned of his master plan. After Lex began to appear more and more unstable, two large factions surfaced in the team leading to an all-out battle between who sided with Grodd and who sided with Luthor. After this battle royale that led eventually to Darkseid's return and an all-out attack on Earth, the League and the Society were forced to work together. With Grodd out in space and Luthor apparently dead, the Society appeared to be no more.
Bruce Timm is known to have stated the all the villains in the DC Animated Universe are intended to be part of the Society, which he refers to as The Legion of Doom. However, certain villains are prevented from doing so, being incapacitated, voted as disincluded, part of a different organization, embargoed, or just generally self-serving.