CFOP (Cross, F2L, OLL, PLL, pronounced C-F-O-P or C-fop) is a 3x3 speedsolving method proposed by several cubers around 1981. It is also known as the Fridrich Method after its popularizer, Jessica Fridrich. In part due to Fridrich's publication of the method on her website in 1995, CFOP has been the most dominant 3x3 speedcubing method since around 2000, with it and its variants used by the vast majority of the top speedcubers.
Origin and Naming Dispute
Jessica Fridrich is often erroneously credited as the sole inventor of CFOP. In reality, developments made in the early 80's by other cubers have contributed to the method in its current form. The constituent techniques and their original proposers are as follows:
Cross: David Singmaster
F2L (4x corner + edge pairs): René Schoof and possibly others
OLL/PLL: Hans Dockhorn, Anneke Treep, with many algorithms developed by Jessica Fridrich
During the resurgence in speedcubing's popularity in the late 90s and early 2000s, there was a general lack of information on the sport. Fridrich's website offered a vast wealth of information for those entering the sport, including a full description of CFOP with complete lists of algorithms. As a result, many who learned from her website began to call this method "the Fridrich Method," which explains the common use of the term today.
Several high-profile cubers have long disputed this terminology; Ron van Bruchem, famously, has publicly written that he will never call CFOP "the Fridrich Method." The issue became well-advertised in the community around 2008. The term "CFOP" has since seen increasing usage, also in part motivated by efforts to standardize terminology in method classification, and is now seen as commonly as "Fridrich Method."
While some cubers still insist on the term "CFOP," Fridrich's contribution to the popularization of the method is undeniable, and many others accept the term "Fridrich Method" as established terminology and a perfectly valid synonym for "CFOP."
CFOP can be viewed as an advanced version of a Layer-By-Layer method. In particular, it combines some steps of the said method into one by using many more algorithms. Here, we outline pure CFOP without any additional trick.
1. Cross: Make a cross on one side by solving all edges of a given color. Align the edges with the second-layer centers.
2. F2L (First Two Layers): Fill in the four slots between the cross pieces, one slot at a time. Each slot is filled by inserting a corner and its corresponding edge simultaneously. Most of the 41 cases have reasonable intuitive solutions. The completion of this step leaves one with just the last layer, typically placed on top.
3. OLL (Orientation of the Last Layer): Make the entire top side (the last layer) of the cube a solid color. This step consists of 57 nontrivial cases.
4. PLL (Permutation of the Last Layer): Finally, you finish the cube by permuting the top layer of the cube. This step consists of 21 nontrivial cases.
Those new to OLL and PLL break up each step into two. This greatly reduces the number of cases; 2-look OLL has 9 cases, while 2-look PLL has 6.
This method is relatively easy to understand when compared to other methods. Therefore, it is the most tested and most popular method used. It has a reasonable number of algorithms to learn, and sub 15 second averages are definitely possible. This method has been used to set many world records, including the current 3x3 world record single of 3.47 seconds. It takes less thinking than blockbuilding methods because it's more algorithm based.
Learning all of the algorithms takes some time, and it requires a lot of practice to solve the F2L consistently in 10 seconds or less. Also, it has a slightly higher move count when compared to block building methods which would make it a rather poor choice to use for FMC or feet solving.
Speedsolving.com: Fridrich Method - info on its origin.