In 2010 there was a debate between some of the major enterprise software influencers and bloggers on whether single or multi-tenancy was an issue for Software-as-a-Service (SaaS) applications. On the one side was Josh Greenbaum who argued that the type of tenancy should not matter to SaaS users; on the other was Phil Wainewright (here and here) and Dennis Howlett whose views were that multi-tenancy is the only way for SaaS software. This debate is still going on.
Single-tenancy refers to a software configuration (application and database) in which each client has its own underlying application resources. Multi-tenancy is where all clients share the same underlying resources. Multi-tenancy also means that all customers get the same application upgrades and enhancements at the same time, whether they want them or not.