6500K is the same as 6500º Kelvin and refers to a shade of white emitted by a radiating black body like a star. The higher the temperature the bluer the white, the lower the temperature the yellower the white. The color temperature of our sun, for instance, is about 5900K, while the light coming through the window (in the northern hemisphere on a cloudless day) is about 6500K.
People who are trying to match to a printed proof will often set their monitor’s white point to 5000K. Proofing paper is often “yellowish” compare to other papers which contain lots of optical brighteners, and light boxes for critical viewing typically use 5000K lights.
On the other hand, the most important RGB working spaces (sRGB, Adobe RGB, P3) all use D65 as their white point. That’s a good default option if you are not sure which white point to use. You can always try multiple TruHu calibrations with different white point and see which works best for you.
