It's generally a sign that you're running your disks / filesystems overutilized. Retaining 10-20% free space is generally encouraged.

If you do elect to do the "copy out, wipe, copy in" method, you can do this, in general, while not completely losing the use of your system. There are some tricks (union mounts, remounting filesystems) which will allow you to flip between filesystems, in most cases. Specifics will depend on your partitioning scheme, use case, and the filesystems under consideration (usually you'd be dealing with user files under /home, spool or variable files under /var, source trees, etc.).

As the article states, Linux systems generally experience very minimal fragmentation, and dynamically resolve the issue for you, unlike Windows. You can typically run a Linux system for years, given a 10-20% disk reserve, without running into appreciable fragmentation issues. The gains from any sort of manual defragmentation would be minimal compared to the cost of performing the task.