Hello,
Vaults that you see in the Vault Configuration page are logical entities but the physical folders which you have now contain the actual content files (hexadecimal files). You can think of 'Mount' as the bridge between the Vaults which are logical entities and physical folders that contain the content files.
So, if you are re-hosting from one source to target system, please make sure that you have copied all the physical folders (you can call them as Vault folders) from the source system to target system. Any folder that is not copied would cause "Some mounts are not valid" error message to be displayed while you try to validate the mounts.
If you are keeping the entire folder structure of vault folders in the target system to match with the source, then you just need to click on each vault in the vault configuration window, go to Objects-->Validate that is displayed on toolbar on top. A successful validation would result in "Mount validation completed successfully" message.
However, if you are changing the location of the vault folders (for example- if vaults exist on 'D:\' drive on source and you are copying them over to 'E:\' drive on target) then you will need do Update the mount on target system to point to the new location before validating the mounts as described above. In this case, after copying the physical folders, go to the vault configuration window and from Sites-->master-->Root Folders select a root folder. In the right pane of the window existing mount for this root folder will be displayed. Select it, go to Mounts-->'Update Mount' in the toolbar displayed on top of the page. Enter the new location in the 'Root Path' field and click OK.
Hope this helps.
PS: I wanted to attach an image to describe the process but am not able to upload it right now. Please let me know if you still need the image and I will try to upload it from a different browser.