That's a broad question, and the reasons vary from a user to another. Some hate what Apple has become (soldermachine and courageports) in terms of performance/$ and the lack of upgradability, and the worst is Apple doesn't care about it, that's their plan for the future (apparently) and which can be very limiting especially for powerusers, who want a good hardware that they have control over, good software that runs their favorite applications and software, but that's the complete opposite of what Apple offers.
In comes the OSx86 project that started as "Yes I can do that with Apple's software" to "Yep! That's how I want my machine to be". This enabled a lot of people to get macOS on their existing x86 machines (your regular laptop or desktop) and from that came a lot of developers that made the transition and tools to simplify and make macOS usable on those machines. "Hackintosh" as a term came after the community started growing and, as you guessed it, is a mix between "Hack" and "Macintosh".
The objective of this project is to install user's favorite (although arguably less advanced) operating system on their devices. The end reason differs from one another but the route is usually the same. If you're concerned about the legality of things, here is a TLDR: "You're in the gray area."