What exactly is WiFy?

It's a protocol for wireless networking.

OK... the Wi is for wireless. What is the "Fy" and what is the "network" made of... radio waves. Sound waves, what?
What frequencies are we talking about?

Its Fi. WiFi was a term coined from HiFi, but the Fi has no real relevance.

A network (in this usage) is a collection of computing devices that can share resources. The connection can be wired or wireless. WiFi uses the 802.11 (now up to N) protocol for wireless communication. You can find more details about it here: IEEE 802.11, The Working Group Setting the Standards for Wireless LANs