Obviously, this is one of the bussard collectors, or nacelle domes, or whatever the heck you want to call them. Personally, I'm not that fond of the whole bussard concept as it pertains to Trek ships but I guess we're stuck with it at this point.
The way they look or what they are?
Originally the Bussard Collectors weren't Bussard Collectors at all. Originally the nacelles is where the matter/anti-matter reactors were. Each nacelles had two warp coils; one in front, and on back. In the back is the white sphere that is the space-time expander. This expanded space-time, enlarged it. Then there was coil on the front, the orange nacelle caps, aka the space-time sink. The space-time sink crunched, or shrank space-time in front of the ship.
This came first from Jeffries design, who set up the matter/anti-matter reactors in the nacelles, keeping it and any harmful radiation of it and other reactions as far away as possible from the crew. What exactly the nacelle caps were he never specified, except that it was part of the engine.
The space-time sink came for Franz Joseph's technical manual, and here came the problem, that was two-fold:
1. Gene Roddenberry wanted to see money, Joseph's manual didn't make him money. So he decided to change things.
2. The TNG guys missunderstood "space-time sink" thinking it was something that collected something from space, and they made it hydrogen.
The nacelle caps on the original Enterprise then have the twirling around concept, while TNG just had a similarly looking red caps.
Interestingly enough, they don't contradict one-another. At the time of TMP, as one can see in the movies, there is no red nacelle caps at all. The ships had neither the space-time sinks, nor the Bussard collectors. The TMP nacelles also don't have the matter/anti-matter reactors anymore, now a central warp core. In order words, the Federation learned the ability of serially putting in multiple warp coils to make the warp engines more efficient.
Only several decades later would Bussard collectors added, who were deliberately or coincidentally made to look like the old warp coils; thus showing a design lineage.
I always figured that the dark orange lanes twirling around in the nacelle cap weren't so much machinery, but rapidly twirling plasma streamers. Maybe you can see how that looks; swirling plasma, making the entire nacelle-cap churning with power.