I just bought a Nikon 50mm f1.2 lens. I have heard/seen people say I will need an adapter for it, why and what adapter?

I have a Nikon d750

No need adapter, but if you bought a pre ai lens, you need to modified it a bit to fit your camera.

Your camera is F mount, the lens is F mount. No "adaptor" needed.

You do realize, however, it is a MANUAL FOCUS lens. NO AUTO FOCUS.

Nikon 50mm f/1.2 AI-S?

It should work without an adapter on your camera. The lens has an F-mount so it will fit as is. You will have to enter the focal length and aperture size in the menu though to use matrix metering and yes, focus is manual.