There are three common acronyms at Rotary that are important to know:  

  • RI - Rotary International
  • TRF - The Rotary Foundation (of RI)
  • PHF - Paul Harris Fellow
RI ... Rotary International, the organization that each Rotarian, Club, Cluster, District and Zone is a member of. The RI global headquarters are located in Evanston, Illinois, about 15 miles north of Chicago.
TRF ... The Rotary Foundation is the charitable arm of Rotary International. It is an endowment fund that manages donations and funding for global projects like polio eradication, promoting peace, providing clean water and sanitation, improving the environment, etc. When Rotary Clubs identify a project that they want to support to make the world a better place, they can apply to TRF for a global grant to match the funds already raised by the club(s) for that project. That's why it is so important to donate to TRF ... to help fund life-changing projects.
PHF ... Paul Harris Fellow. Paul Harris was the founder of Rotary, back in 1905. In his memory, the PHF award recognizes a donor's overall contribution of US$1,000 to The Rotary Foundation. Upon reaching this milestone (which can be done in increments over time, or all at once), the donor receives a special "Paul Harris Fellow" (PHF) Rotary pin and a certificate of appreciation. The donor's PHF designation is also added to their personal Rotary profile as well as to Rotary International's list of PHF honourees.
Over time, some donors reach the PHF threshhold multiple times, and Rotary then provides a new pin with gemstones to indicate the number of times. For example, here is a pin for a donor's five-time PHF recognition. 
Each US dollar donated to The Rotary Foundation earns the donor one PHF "point", and when 1,000 points have accumulated, the PHF award is given.  
Some multiple-PHF donors are less interested in getting an additional pin and prefer to "donate" their extra PHF qualifications to their club for the purpose of awarding an Honourary PHF to recognize a worthy individual for their contribution. 
An Honourary Paul Harris Fellowship award, named after the founder of Rotary, is one of the highest honours that Rotary International can bestow upon a person. It recognizes recipients for their outstanding contributions that exemplify the highest ideal in Rotary of delivering “SERVICE ABOVE SELF.”
Separate from the above is the Paul Harris Society, whose members donate at least US$1,000 annually to The Rotary Foundation.  More information may be found here