For most large web applications, uptime is of foremost importants. Any outage can be seen by customers as a frustration, or opportunity to move to a competitor. What's more for a site that also includes e-commerce, it can mean real lost sales.
Zero Downtime describes a site without service interruption. To achieve such lofty goals, redundancy becomes a critical requirement at every level of your infrastructure. If you're using cloud hosting, are you redundant to alternate availability zones and regions? Are you using geographically distributed load balancing? Do you have multiple clustered databases on the backend, and multiple webservers load balanced.
All of these requirements will increase uptime, but may not bring you close to zero downtime. For that you'll need thorough testing. The solution is to pull the trigger on sections of your infrastructure, and prove that it fails over quickly without noticeable outage. The ultimate test is the outage itself.