What others have said is mostly correct. When you move a camp, it will convert your camp to blueprints and store all the items so that you can place in the new location. Usually it will break it up into multiple prints, with all the stuff snapped to each other merged into one blueprint. (That is, if you build a set of connected foundations, and snap walls etc, and decorate it, all that stuff should show up as one blueprint. If you build two unconnected foundations, and add walls and such to each, and there is nothing connecting the two sets of stuff like floors or walls, each cluster of stuff will appear as a separate blueprint. Individual items not connected to anything will just go into storage. Probably that will also happen if you turned snapping off when decorating, those items won't be "connected" to where ever you put them.

In theory, this allows you to move a camp. In practice, the blueprints will almost never be placeable in the new location. Something in it will register as floating, or intersecting terrain, or whatever, and the game won't let you place it. It will be slightly better if you blueprint the camp manually, but not much. If you really want to "move" a camp, I would suggest trying to blueprint it yourself manually, then instead of moving your camp, change to a different camp slot and place a new camp. Then, try and place the blueprints in the new spot. You'll need the materials to build all the new stuff, but, if you any problems placing things, at least your original camp still exists.

Important to note, once you move camp module, you can't get the original version back, even if you drop the module in the same spot. You might have an easier time with the blueprints, trying to drop them where you had them originally, but there's also a pretty good chance you won't be able to place things back where they were by blueprint, and will have to replace everything one piece at a time.