They say a picture is worth a thousand words...
Beast Mode (ビーストモード), in the Rebuild of Evangelion continuity, is a special built-in combat function that gives an Eva pilot access to more of an Eva's innate power, resembling a "controlled berserk". Eva-02 is the only unit shown to have this capacity.
In Evangelion 2.0, the mode is showcased when Mari pilots Eva-02 against the Tenth Angel. After traditional combat methods prove ineffective, she initiates the process by saying, "Invert mode. Secret code: The Beast!" This jettisons the shoulder pylons, painfully releases the Eva's restrictors, and triggers a physical transformation wherein the Eva "abandons its humanity". The Eva's body proportions are generally elongated, and the head becomes saurian in appearance, with a large maw and uniformly shaped teeth. By the end of the transformation, many of the Eva's outfittings are missing or otherwise altered. The reconfigured Eva is still controlled by the pilot and relies on internal battery power, but exhibits vastly heightened mobility and A.T. Field-breaching power.
Both the Eva and its pilot behave in a very animalistic manner. Activating Beast Mode seems to be very taxing on the pilot, and entails a negative plug depth that puts her at great risk for losing human form herself. The only immediate physical change that Mari experiences as a result of the venture are glowing green irises. However, in *Eva 3.0*, she appears to be suffering from the "Curse of Eva" much as Asuka, having not aged at all in fourteen years -- likely the long-term consequence of using Beast Mode, due to the risks associated with excessive plug depth.
In Evangelion 3.0, Asuka's revamped Unit-02 showcases new variations upon Beast Mode which are triggered via the verbal command "Code 777 (read as "Triple Seven")". Two distinct stages are seen. In the first, some of the armor plating along with the internal restrictors are explosively jettisoned and the Eva's mouth opens; the result physically resembles an Eva-02 version of the berserk Eva-01 seen at the end of episode 19 of the TV series. Soon after this, the second stage sets in, wherein Eva-02 transforms into a giant saber-toothed leonine creature, exhibiting the same enhanced strength and agility as the beast form from 2.0. Asuka gains feline features herself, such as fangs and slit pupils, and her eyes glow.
The term "Beast Mode" is not used within the film itself, but rapidly entered the fan parlance. It appears on the packaging of a set of Eva figurines released by HDM Souzetsu, and possibly other merchandise, which gives "Beast Mode" sufficient authenticity.
The full term for the mode seen in Evangelion 2.0 is Beast Form 2nd Phase (Type 1) (獣化第２形態（第１種）, Juuka Dai 2 Keitai (Dai 1 Shu)). This raises the questions of what "1st Phase" would refer to, or what the other implied "types" are. It's not known at this time what the full designation of the version seen in 3.0 is.
- This is not well-explained. The one cut addressing it simply shows the plates on Eva-02's back vanishing, as by "sinking into" a dark matrix from which the limiters then eject.
- Full Color Market. HDM創絶エヴァンゲリヲン新劇場版2 ｓｐ入全9種フルコンプ. Retrieved 2011-02-03.
- Translation from Evangelion 2.0 Complete Records Collection.