I need a 25 ft HDMI cable to go from my DISH 622 and HDTV. Monoprice has them with or without FERRITE CORES. What's the difference?

They keep the square-wave data signals from leaking RF spectrum energy all over the place. Square waves have almost infinite noise bandwidth, and will cause interference to all your nearby radios and TVs.

A lack of ferrites might indicate that they have sufficient shielding to prevent interference, or that they are "clean" enough to meet some FCC Part-15 specs (but, could still interfere to some extent), but I wouldn't trust it. Ferrites are pretty cheap to make, anyway....good insurance.