Resource units (RUs) are a pseudo-currency used at Earth Starbase for "buying" fuel, modules, ships, and crew. They represent the amount of resources available for The Captain to use in his fight against the Ur-Quan Hierarchy. Because RUs are simply a handy way for The Captain to keep track of resources, and not a true currency that is exchanged for goods and services, everything purchased at Starbase can be "sold" back at cost.
You also get RUs by destroying enemy ships ("Spoils of War") — the scrap materials will be scavenged automatically and will be immediately available as RU. No Storage Bay is required for this. You do not get RUs when your own ships are destroyed.
Once you have agreed to install the Utwig Bomb in the Flagship, the Chmmr will give The Captain large amounts of resources, essentially providing unlimited RUs. Commander Hayes even comments on this after the bomb is installed.
See also: Interstar Credits