According to Cinema Blend on Dec 5, director Marc Webb and other cast members of "The Amazing Spider-Man 2" break down and talk about certain shots in the trailer. Apparently a short clip teased a lot of imagery that gave a quick glimpse into what fans would be expecting.
Webb talks about how certain villains like Rhino, played by Paul Giamatti, would probably not translate into this current world so well, that being said, they figured I'd be best to adapt the character into a machine-like construct but with similar intellect. The director of the film also, without revealing too much about the plot, informs his fans both the past and future of Peter Parker, played by Andrew Garfield.
"Peter learns certain things about his past that will inform his future in very provocative ways".
There are also certain glimpse of villains such as the Vulture's wings or Doctor Octopus' mechanical tentacles that tease the audience of what Spider-Man may be up against. Then of course there is Electro, played by that most fans have been aware of up until this point.
In a basic summation, it appears that trailer tells a story about Oscorp had used Peter's father's research to develop troubling research that he'll have to face in opposition as Spider-Man. As Webb puts it:
"There are very powerful forces at work that are eminating from Oscorp. Oscorp is a place where all things...all nasty things merge in this movie".
"The Amazing Spider-Man 2" is scheduled to be released May 2, 2014.