The Starship Enterprise of Star Trek: The Original Series is around 300 meters in length. It's one thing to know this, it's another thing entirely to have a sense of what that means. That's why ParkMySpaceship.com is one of the coolest websites out there; the site plugs into Google Earth and allows you to superimpose the Enterprise and other fictional vessels over any location that's familiar to you.
For instance, thanks to ParkMySpace.com, I know that if the Enterprise were hovering over my apartment building, the tip of the saucer section would be at one end of the apartment complex, the engineering section would be over the library next door, and the nacelles would stretch past the gym next to the library, and their tips would be at the end of the playground next to the gym.
Other ships of the Star Trek universe available in ParkMySpceship include the Enterprise-A, the Enterprise-D, Deep Space Nine, The Defiant, The Voyager, and a Borg Cube. Though DS9 and the Borg Cube broke my brain a little, as even a useful app like ParkMySpaceship can't make their size digestible. With DS9 at almost one and a half kilometers, and the Borg Cube at over three kilometers, seeing them over a familiar building or neighborhood doesn't help, these massive structures are on the scale of a city.
It might surprise you to learn that there is still no official canonical size for the Enterprise. Size estimates put it at around 300 meters, with the most common given length as 288.6 meters. This prompts the question, how would one go about estimating the size of a fictional ship? And perhaps more importantly, why?
The first question is a little complicated. According to this fantastic article from Ex Astris Scientia, the factors one must consider when estimating the size of a ship include the number of decks shown on the ship diagrams on the Master System Displays, and the number of windows visible on the exterior.
Of course, since these estimates are unofficial, there are inconsistencies, such as disagreement about the size of the Defiant ranging from 50 to 170 meters, and inconsistent accounts about the size of the Kelvin Universe Enterprise, ranging from just slightly larger than the original to 762 meters, or the ongoing debate about whether you could fit two humpback whales into the cargo hold of a Klingon Bird of Prey.
"Why" is an even more complicated question, but it comes down to what made us all love Star Trek. Star Trek is its own fully realized and lived-in universe. Even in the first few episodes of the original series, Star Trek felt like a real place. It was one thing to have such a hopeful vision of the future, it was another to have a vision that we could believe in.
So, to complete that vision, fans naturally filled in every missing detail and oversight. If any piece of information about the Star Trek universe was not provided onscreen, the fans were there to ensure that nothing was unknowable. The current crop of Star Trek shows is produced and written by people who love the franchise, fans who get to see their contributions to the lore onscreen. Star Trek fandom is an ongoing communal project to make a TV show as close to a real place as possible.