PC-Free printing refers to the ability of a printer to print photo's without a PC, for example from your phone via bluetooth, or from a memory card from your camera or phone, or from a smart device with Wi-Fi. Most support one of the most common formats, JPG, some support additional file formats.
They have a small built-in display that allows you to see the picture before you print it and to even make adjustments, like rotating it, darken/brighten, adjust the color, and crop the photo.
Even if you have a PC this can be handy to quickly and simply print a picture from say your phone, no need to transfer it to the PC and print it from there, just send it wirelessly or through a memory card to the printer, get it how you want and press "go".