Tesseract
Tesseract
The unofficial (official?) name of the cross-shaped container that contains Unit-01 found at the beginning of Evangelion 3.0, floating in low orbit above a damaged Earth. The Tesseract unfolds to reveal several long tentacle-like arms made of metallic squares, which light up and begin to attack Unit-02'. Upon Unit-01's Awakening, the arms are destroyed, but the Unit remains inside the Tesseract for the duration of its appearance on screen. It is unknown when and how Unit-01 was retrieved upon returning from orbit.
Purpose
The Tesseract's owner is unknown. Because of the time skip between films, it is unknown what organization put Unit-01 into it and then decided to keep it in orbit. It is evidenced from the various difficulties during Operation US that the intention was to make retrieval of Unit-01 difficult, and that placing the Unit in orbit was a known way to keep Wille from obtaining it. It is also possible that Wille was the one to do it, and that somehow, keeping Unit-01 in orbit was necessary.
The various implications of the Tesseract and its placement show that whoever restrained Eva-01 found Shinji's distance from Earth necessary. It's possible that there was a recurring fear of another Impact, and so keeping Shinji from Earth would prevent the disastrous effects thereof once again. However, Wille's need to retrieve Shinji directly contradicts this, as the risk of bringing Eva-01 back to Earth also contradict their very purpose--to prevent more Impacts. However, Misato mentions in 3.0 that Wille will "ensure your safety" to Shinji. It's then possible that Wille retrieved Unit-01 to get Shinji out of it, thus inhibiting an Impact, where Nerv may have gotten to the Tesseract first to initiate it.
Technology
The Tesseract appears as eight cubes combined to form a cross-like structure, with what appears to be a fence-like structure on the bottommost portion of the device. In contrast to other crosses that appear in Evangelion canon, which are bright, thin and sport a rainbow, this cross in particular is black, solid and is a symbol of restraint, not victory.
One of the arms opens up and unfolds into four square-based tentacles that are metallic on the other side, and the other arms open up as well. Inside each arm appears to be a Nemesis Series drone, which Unit-01 then destroys. It can be assumed that these were traps set for anyone wishing to release Unit-01 and not an integral part of the system.
Upon cracking open, Unit-01's eye can be seen glaring at Unit-02', surrounded by red matter, not unlike the environment of Third Impact. The inside appears very distorted and the nature of its contents cannot be known. Exactly what mechanisms are in place to restrain Unit-01 and how they prevent activity are also unknown.