Spider-Man Suit

"Well, I could've stuck the landing a little better. It's just the new suit- it's nothing! Mr. Stark, it's perfect, thank you."

- Spider-Man to Iron Man

The Spider-Man Suit is a specialized suit created by Tony Stark to help Peter Parker focus and control his powers and also to protect his identity.

Homemade Suit
"You're the Spiderling? Crime-Fighting-Spider? Spider-Boy?" "...S-Spider-Man." "Not in that onesie you're not." "It's not a onesie."

- Tony Stark and Peter Parker

Originally, Peter Parker wore a homemade suit consisting of cheap red and blue clothing such as a blue onesie-like suit with a red hoodie over the top with the sleeves ripped off and a black spider on the chest, red fingerless gloves with black webbing designs on them and black squinted goggles to fight crime in New York City; he hid this suit from his aunt May by hiding it in a loft above his room which came down on a rope whenever someone opened it. Parker apparently abandoned this suit when Tony Stark visited him and decided to make him a new suit after jokingly mocking it.

New Suit
"You're in dire need of an upgrade. Systemic, top to bottom."

- Tony Stark to Peter Parker

Tony Stark constructed a new-and-improved suit for Peter Parker after visiting him and seeing the old costume he used to fight crime as Spider-Man. This new suit was more tight fitting and the exact same color as his old suit. He used this suit at the Clash of the Avengers to fight Captain America's faction.

"I get to keep the suit?" "'Course. Doesn't fit me."

- Peter Parker and Tony Stark

After returning from Germany, Tony Stark allowed Peter to keep the Spider-Man suit, on the condition that he does not attract attention to himself and remains close to the ground.

"Look, I'm going to need the suit back." "But I'm nothing without the suit!" "If you're nothing without the suit, you don't deserve it."

- Iron Man and Spider-Man

After a confrontation with the Vulture where the villain put several civilians in jeopardy, Tony Stark asked Peter to give him back the suit, deeming him to be to irresponsible and not earning the right to wear it.

Original Suit

 * Web-Shooters: The suit has Web-Shooters strapped onto the wrists that allow Spider-Man to discharge synthetic webbing for various purposes. It is presumed that the web-shooters were made from old parts that Peter got from the garbage. These were the only part of the costume which Tony Stark didn't mock.
 * Black Goggles: Peter relied on wearing black goggles which had little slits in the lenses for Peter to see out of, Tony Stark mocked these while putting them on, quoting 'Lordy! Can you even see in these?', to which Peter replied that he could see in them and that they helped him to focus, stating that his senses had been 'dialed up to 11'.

Upgraded Suit

 * Eye Lenses: Spider-Man's eye lenses appear to be modeled after camera shutters, giving him a squinting look when they close in and provide him a greater depth of field. This mechanism also helps Parker filter out extra stimuli.
 * Upgraded Web-Shooters: The suit has Web-Shooters strapped onto the wrists that allow Spider-Man to discharge synthetic webbing for various purposes. These shooters were more modern and streamlined. It was revealed that a mechanism within the Web-Shooters allows Spider-Man to display a Spider-Signal with the motif of his mask.
 * Utility Belt: The belt attached to the suit can hold at least six spare web-cartridges used as refill for Spider-Man's web-shooters.
 * Web Wings: An upgrade from Tony Stark that allows him to glide in the air with a pair of wings that spread from his armpits and extend to his upper arms and thighs, it appears that they can be retracted for when he doesn't need them and only uses them for when he's too high or not enough places for him to swing from.
 * Suiting Up Process: By pressing the emblem on the chest, Peter can have the suit expand and become several sizes larger, allowing him to slip out of the suit easily. It appears that he can still wear his regular clothes such as boxer shorts under the suit due to the same process compressing the suit, making it appear as though he's not wearing anything underneath.
 * Spider-Tracer: In addition to altering the suit's size, the spider emblem on his chest is capable of detactching from it's socket, deploying miniature rotating blades from it's tail section that allow it to fly through the air, seemingly independent of Spider-Man's control. It has a drone mode which allows it to fly onto a target and act as a tracking device.
 * GPS Tracking System: On his right forearm, Parker has a GPS tracking system with a holographic display, allowing him to follow his Spider-Tracer.

Trivia

 * In the comics, Peter Parker created his Spider-Man suit himself, while Tony Stark created the Iron Spider Armor for him during the Civil War.
 * The camera shutter-like eye lenses may refer to Peter Parker's occupation as a freelance photographer for the Daily Bugle in the comics. It can also refer to numerous times in the comics where his eye lenses would show expressions by widening or squinting even though he's wearing a cloth mask.
 * His original suit, before the upgrade by Tony Stark, matches that of the Scarlet Spider suit from the comics. Albeit with an inverted color palette.

Behind the Scenes

 * The suit's design is inspired by the classic era Spider-Man costume.
 * The suit was mostly a CGI creation for Captain America: Civil War, but an actual costume was created for Spider-Man: Homecoming, to be worn by Tom Holland.
 * The suit has been shown to house hidden protocols that enable special features, as hinted at in the post-credit scene of Captain America: Civil War. The trailers for Spider-Man: Homecoming show Peter and his best friend, Ned Leeds seemingly trying to access the suit's systems to discover these features.