The suit is real.
The newest (this is the 3rd time in 14 years, it's hard to believe they will ever stop) Spider-Man costume is very different from the previous 2two. It highly resembles the comics in design.
According to Marvel Chief Creative Officer, Joe Quesada, the costume creation followed a traditional line.
It looks awesome. I’ve seen a lot of design work that’s been done on the costume. I think there are elements of it that are really going to blow people away, where they are going to go ‘Ah, that’s Marvel doing Spider-Man.' - Source
You can also find on (supposedly belonging to) Russo Bros' Twitter account that they shared some details from the suit.
But people seem to take the picture not seriously (some say this is from a basketball). Because there was another one that resembled a coffee mug.
A few months ago Marvel Studios President Kevin Feige said the suit was "different than any of the ones that have come before."
I was more involved in the Raimi ones, and think they did a very good job. But that being said, we’ve already designed the costume, which is different than any of the ones that have come before. And yet ours is classic Spidey, as I think you’ll see. - Source
As you probably realized the eyes of the suit is CGI, because they are expressive which is a first in any of those previous debuts. Also the logo on his chest is different (smaller). And there is some sort of belt around the waist.
I do not remember the source but I watched an interview few weeks ago and it was said some CG applied to improve the suit. So I take it as "the suit is real, some improvements were done with CGI."
Anyway, I believe Tony (Stark) is behind the creation of this suit (to lure Peter Parker in).
- Avengers Vol. 5 #2 (not related with the topic but this is just too good to ignore)