It looks like some kind of suction cup, perhaps. Which would be weird, as Spider-Man’s wall-crawling ability is innate. But what if it’s just a hole in the glove intended to allow the mechanism of his wall crawling to work? In the comics Spider-Man’s ability is ill-explained; it’s been laid down to a sub-atomic manipulation that increases the coefficient of friction, while Spider-Girl, who has the same powers, has been said to have ‘bio-magnetism.’ In the comics it isn’t just Spidey’s hands and feet that stick - we’ve seen him actually use his back.
But what if the new movie Spidey has microscopic hairs on his finger tips, a la the previous film incarnation and a la real spiders? These holes could be places where the hairs are able to poke out and thus allow him to stick to objects. Or, since the film seems to be taking a costume page from Spider-Man 2099, maybe this Spider-Man will have angled talons in his fingers and toes.
Whatever the case, this is an obvious example of highly nerdish attention to detail on the part of Marc Webb and the good people behind The Amazing Spider-Man. I approve!
Thanks to @aliarikan for bringing this to my attention.