What does hardening off mean?

Your question has two answers, and maybe more. As with regard to the roots of a plant, it refers to larger trees that are designed to be relocated either from a nursery or within a landscape, whereupon the plant or tree needs to "rest" for a time, to regenerate new roots that will make the transplant more successful. Generally, the tree or large bush is dug, and sits in place with additional irrigation, with the hope that is will generate new roots. And, then after a designated time, it is moved to it's new location.

The other term off hardening off refers to plant trimming, prior to winter, or even fertilization, whereupon you coax new growth, in the attempt that new growth will turn from tender to adult leaf, prior to a potential freeze. Seedlings also harden off, but I can't say about that.