The Takedown Pin is located at the rear of the lower receiver, near the buffer tube, and assists the pivot pin in securing the upper and lower receivers together.
Once removed, the takedown pin allows the upper receiver to pivot on the front pin, while exposing the interior parts of the AR-15.
An excerpt from the FSD Blog, “Let’s Twist Again”:
In layman’s terms, the twist rate is the number of revolutions the rifling makes inside the barrel.
Think of a Slinky (younger folks, look it up). The spiraling of the toy is what it’d look like if you took away the outer metal of the barrel and only left the lands and grooves inside. You can stretch it out so that the spirals appear farther apart, or mash it together and the spirals will compact. The spirals in a Slinky are the revolutions we’re talking about.
The more times the spiral makes a full revolution, the lower the twist rate. For example, a 1:9 (to be read “one in nine”) twist rate means that, for every 9 inches, the rifling makes one complete revolution inside the barrel.
When it all comes down to it, we’re really talking about stabilizing bullets. That is, taking into account the air that the bullet must pass through and figuring out how long the bullet will remain stable.
The numbers of revolutions made inside a barrel determine the stability of the bullet. So, the lower the number, the more (and sometimes faster) the bullet is spinning, the more stable the bullet is.
For an AR-15, the upper receiver is the part of the firearm that houses the charging handle, bolt carrier group, and in some receivers also the forward assist and dust cover. Newer models of the upper receiver may also have the charging handle integrated into the receiver, rather than as a stand-alone part.
Most upper receivers also have a brass/shell deflector. However, some competition-level receivers do not.
Conversely, some upper receivers in an A1 or A2 configuration have fixed carry handle on top, while other receivers like the A3 or A4 do not.
The upper receiver also connects the barrel and handguard to the lower receiver, as well as connecting to the lower receiver to complete the firearm.