mount namespaces differ in the arrangement of mounted filesystems.
This is very flexible, because mounts can be bind mounts of a sub-directory within a filesystem.
# unshare --mount
# mount --bind /usr/bin/ /mnt/
# ls /mnt/cp
/mnt/cp
# exit
# ls /mnt/cp
ls: cannot access '/mnt/cp': No such file or directory
You can list your current set of mounts with the findmnt command.
In a full container, the root mount is replaced and you work with an entirely separate tree of mounts. This involves some extra details, such as the pivot_root() system call. You probably don't need to know exactly how to do that. Some details are available here: How to perform chroot with Linux namespaces?