Relay - A device that contains a coil and a set of contacts which close when the coil is activated.
DPST (Double Pole Single Throw) - A four-terminal switch or relay that can open or close two separate circuits. Essentially, two SPST switches or relays combined into a single component.
Your understanding is correct. It connects one (or more) switched circuits when power is applied to it. So, a relay with two contacts, one for 1-3 and one for 2-6, will work for you. You'll need one with a coil that handles 12 volts. Radio Shack has several. This site will also help you understand relays: http://www.the12volt.com/relays/relays.asp.