According to Wiktionary, continuity means lack of interruption or disconnection; the quality of being continuous in space or time.
Think of it. Lack of interruption in a real-world context means being able to withstand interference, continuing [sic!] to function in the face of external events. What kind of events? Some will be anticipated and we can design our system (process? service?) for them. Some will be unforeseen. How can we design for the unexpected? We know we have to.
What is continuity to you?