A custom ROM is a tweaked ROM fully standalone version of the OS, including the kernel (which makes everything run), apps, services, etc. - everything you need to operate the device, except it's customized in some way. Custom ROM gives user power to customize apps thus improving the overall performance of device.
The most basic benefit of custom ROMs is getting rid of “bloatware” — the trial or otherwise unwanted software carriers often include in the ROM to get you to buy more stuff that you may not need, and that takes up precious room on your device. The first thing they leave out is the space-consuming trial software. They may also leave out many of the included utilities, letting their users add them back only if they need them.
The availability of custom ROM for specific device depends upon the popularity of that device among Android developers and users. If the device is not that much popular, then you will hardly find a good custom ROM for that device while on the other hand there will tons of custom ROM available for device like Samsung Galaxy S3 or S4, HTC One etc.