Air, heat and speed
Air slows a rocket on the way up and burns it on the way back down. Shape decides how much of each: a pointed nose and folded fins lose less to drag, and whatever meets the air first is what takes the heat.
Drag
Every part shoves air out of its way, and a part shaped for it pays far less for that than a blunt one at the same speed. A nose cone capping the top of a stack shadows everything behind it from the airflow at almost no drag cost of its own, so it earns its place on a stack even though it does nothing else. Fins and wings further down trade a little of that shadow for the lift and the turning bite they give you. Two rockets with the same engine climb at different rates once one of them is capped and the other is not.
Why an engine pushes harder in vacuum
An engine's bell pushes against the air behind it, so the same flow of propellant makes less thrust low down in thick air than it does once the ship has climbed past it. Every engine's card quotes both ends: the Engine makes 215 kN at sea level and 250 kN in vacuum. How far a kilogram of propellant pushes the ship is its Isp, which for the same engine rises from 290 s to 338 s across that same climb. A bell built wide for vacuum work loses more of that than a narrow sea-level one does, which is why a vacuum engine can lag badly at the pad and still out-run everything else once the air is gone. Engines has every engine's range.
The sound barrier
Crossing the speed of sound costs more than the speeds on either side of it. The air ahead can no longer get out of the way in advance. It piles up instead into a cone that trails the ship, a faint shockwave visible in the sky, while the climb briefly fights hardest against the throttle before it breaks through.
Skin heating
Air moving fast enough against a part heats its skin, and every part has its own limit past which it comes apart. The info card's MAX TEMP row is that limit: a Wing tolerates only 345 K, enough to go supersonic high up but not low down, where a plain fuel tank tolerates 1300 K before the same thing happens to it. As a part nears its limit it glows first, then trails plasma and sparks the hotter it runs, so the ship is warning you before anything actually fails. A bare tank flown fast and low, with nothing ahead of it to shadow its nose from the airflow, can overheat and come apart long before it reaches orbit.
The heat shield
The Heat Shield survives what nothing else can, and it does not resist heat so much as spend itself against it. Flown facing down into the airflow, its dish shadows whatever rides behind it and boils away its own Ablation in proportion to how hot it runs, which is what buys it a limit of 3600 K that would destroy almost any other part. Once the Ablation is gone the dish is a bare plate, worse than flat, and it heats like anything else on the ship from then on. It buys you one hard re-entry, not an unlimited number of them.
What a fairing or payload bay shelters
A Payload Fairing is a shell you shape from rings in the hangar, and only a payload standing entirely inside its narrowest ring counts as sheltered from the airflow. One that clears the base but pokes out through the nose is a breach: the hangar names the offending part on the mass line the moment it happens, and a breached shell breaks apart at launch instead of protecting a hole in itself. A Payload Bay is more forgiving: its doors simply stay open around whatever rides inside it, so nothing there can breach it.
Every part's own drag, heating and thrust figures are in Engines and Aero parts.