In a simplistic answer I would say:

Home is for private, home or school use with basic operational security. Pro is for professional use of the operating system in a business or office, where security, system administration and its integration into teamwork with other computers is important to be done effectively.

Internally, perhaps most noticeably, the Pro version offers better options for secure connectivity in a networked environment and the internet. Data encryption and other issues that are of high importance for security in a business environment.