Office 365 is technically referred to as software as a service (SaaS). This can be scary for some IT professionals who are used to running their software locally and having complete control over it. This new model does offer benefits however, such as constant maintenance, access from everywhere, and secure backups. Microsoft is attempting to alleviate some of the pains of using Office 365 by making it faster and more stable to use.
There are many steps which form the connection between Microsoft and a customer's PC. Microsoft only has control of a few, so to make the connection better they must keep their part of the connection lightning fast. Microsoft keeps adding servers to improve their capacity for their users. They are also tuning and improving the connection between their servers and the public internet.
Other than what Microsoft can control, they can speed up their service by educating IT staff. Office 365 may be a SaaS, but there are steps a company's IT can take to improve their employee's connection. A major component of this education is communicating what type of internet connection will deliver a good experience. Also ensuring the company has proper security settings to allow for a complete experience. Microsoft is also training IT on how to troubleshoot a bad connection.
All of these courses are available to IT departments from Microsoft's Virtual Academy. These courses are part of the overall plan to partner with companies to transition them to the cloud. Many companies feel timid about moving their servers off premises where they have less control over it. While it may be true some servers are moved off premises, ultimately now, their servers can be managed directly by the best people in the business. On premises servers may only offer the illusion of control, while the major factors which control IT health and security were always out of the hands of a company's IT staff.