I'm not going to try and fully explain it, as I'm not 100% clear myself, but for your purposes:
A characteristic represents a particular value. It can be readable (on demand), writable, or it can notify you when it changes.
Characteristics are grouped together in a Service.
Services and characteristics are identified by UUIDs, which can be either 16bit (e.g. "2221") or 128bit (e.g. "abece8fd-afde-40b4-b1b1-632adfb84d5e"). The 16bit UUIDs are reserved for registered official uses, which is probably what that documentation page is referring to. The 128bit UUIDs are supposed to be random enough not to overlap, so there's no need for central registration.
Typically there is one "main" Service that a BLE peripheral advertises, in RFduino it is 2220. You would ask Windows phone to find BLE peripherals advertising the Service "2220" and then pick one to connect to. Once the Windows phone connects it must scan to discover all the Services; it should find 2220. Now it must scan that service for Characteristics; it should find 2221, 2222, and 2223. One of those Characteristics will be marked as capable of being transmitted to, another will be marked as capable of sending notifications. You need to ask Windows phone to enable notification for that characteristic, that will be how you RX data from RFduino whenever it is sent. The third is unimportant.