Continuity is a great collection of features. To work, it cleverly uses Bluetooth or Wi-Fi depending on what makes the most sense for the job. Also, sometimes the devices have to be on the same network, other times not. In the linked post on Ars Technica, Iljitsch van Beijnum details the various network requirements behind each Continuity feature. For a less detailed summary, there's this handy tweet:
— Michael Jurewitz (@Jury) October 21, 2014
Related: Continuity also has various hardware requirements which can be found in this Apple support article.
[Michael Jurewitz tweet via pavan rajam]