This New Element is an element researched and theorized by Howard Stark, and later synthesized by Tony Stark as a replacement for the palladium core in his Arc Reactor, which had been poisoning him. The element generates power similar to that of the Tesseract, which Howard Stark found and studied in the years following World War II.
Following his recovery of the Tesseract from the bottom of the ocean, Howard Stark began closely researching the object as he believed it to be the key to limitless, renewable, clean energy. During the course of his study of the object, Howard theorized a new element structure that could partially replicate the energy of the Tesseract.
However, limited by the technology of his time, Howard was unable to create the element for himself and instead left the blueprints for the element hidden in a model of the Stark Expo fairgrounds for his son Tony to discover later. Evidence of Howard's research with the Tesseract was later indicated through several drawings of a hypercube, a theoretical representation of the Tesseract, spread throughout many of his research notes.
In the months following Tony Stark's continued activities as the armored hero Iron Man, he became afflicted with palladium poisoning from the degrading palladium cores from the Arc Reactor embedded in his chest, accelerated by the continued use of his Armored Suit. Tony sought to find a replacement material for the reactor's core, but no known element was compatible with the Arc Reactor.
S.H.I.E.L.D. became aware of his problem and Nick Fury gave him a package that once belonged to his father. In the box was a film reel where Howard strongly suggested that there was something hidden in a model of the Stark Expo. He discovered that the buildings in the model formed the atomic structure of a new element. He recreated the element by using a Particle Accelerator in his basement and created a brand new Arc Reactor to utilize the new core and a new suit that could better utilize the higher energy output.He later tried to get it patented as "badassium" but ran into many legal issues.
It remains to be seen if Tony uses the new element to power his Iron Legion drones, or he has simply resume use of palladium for constructing arc reactors for the drones, due to both the drones not requiring technology as advanced as the armors he personally dons, and palladium poisoning not being a concern at all.