The “Bucket Repeater” is a battery powered cross-band VHF/UHF repeater in a weather proof enclosure that can operate unattended for a week or more, and be remotely activated or deactivated from miles away as needed.
I will say that he's probably get better performance by substituting a 1/4 ground plane or copper J-pole for the magnet mount antenna. The latter has the advantage of easy mounting, not to mention the fact that you can buy a decent one from Amazon for around $20, already assembled.
A cross-band repeater like this is valuable for groups who want to communicate over distances or terrain which would normally block an FM signal. For example, you might have two people who need to communicate via UHF or VHF, but one's home is located in a hollow, the sides of which block the radio signal. A cross-band repeater like the one described in the linked article could be placed up in a tree on an intervening hill, allowing two-way communication.
An alternative if you do not have a radio capable of cross band repeat is a simplex repeater like the MFJ-662 or Argent Data Systems ADS-SR1, which use the store-and-forward technique. A simplex repeater might be easier to setup, but cross band repeaters provide better realtime commo.