The following excerpts are from an article by Yukio Takamura, edited by Nanette Okura. There is a link at the end to read the complete article.

"Shu-ha-ri" literally means embracing the kata, diverging from the kata and discarding the kata. The pursuit of training in a classical Japanese endeavor almost always follows this educational process. This unique approach to learning has existed for centuries in Japan and has been instrumental in the survival of many older Japanese knowledge traditions. These include such diverse pursuits as martial arts, flower arranging, puppetry, theater, poetry, painting, sculpture and weaving.
 
Shoden/ The beginning level of training
 
Shu (Embracing the kata)
The kata or form is the educational core of all traditional Japanese knowledge schools. It is the most visible representation of a schools knowledge packaged into one seemingly simple set of movements or concepts. Because the kata is so accessible it is often mistaken to be the most important aspect of determining a students ability or progress. In fact, properly taught the kata does contain within it the ura or hidden level of information, but this information lies beneath the surface or omote of simple observation.

 

Without first devoting oneself entirely to the mastery of the omote of the kata, the student is destined to remain forever a beginner, never able to progress towards the true depth of knowledge that rests hidden in the ura before him. To experience shu and embrace the kata, the student must first resign himself and his ego to a seemingly random series of repetitious exercises.  In time different neuro-muscular processes become intuitively ingrained in such a way that they are no longer consciously realized by the student.

 

Once this level of kata is absorbed and executed satisfactorily, the student has reached the first level of his or her training. The most basic reason for kata training has been achieved.
 
Chuden / The intermediate level of training
Shu.
At the chuden level kata study includes a new element. This element is the application or bunkai. The deeper reason for the kata and its construction is now presented to the student. The scenario in which the kata exists is also studied and evaluated. This study and evaluation is however strictly limited to the pure execution of the kata without variation. Only thru this strict study can the kata accurately demonstrate its relevance to the student at a level he can comprehend. This paves the way for the second aspect of Shu-ha-ri.
 
Ha (diverging from the kata)
In the traditional Japanese concept of Shu-ha-ri, ha is the first hint of creative expression allowed the student. It is when the henka waza or variation is first experienced. It has been called the "divergent form existing within the form" or the "orthodox variation that co-exists within the confines of the strictly defined greater kata" . This is when the student is encouraged to consider any response to a failure within the pure kata.  The kata must remain recognizable as the kata. If the kata diverges too far from the norm, it is no longer related to the original kata and becomes an altogether different expression of technique. It is imperative that such a deviation be avoided at this level of learning.

Ha, at the chuden level
Once the student discovers the boundaries of his training within the greater kata he will find the possibilities of learning almost endless.  He now more fully appreciates the kata and recognizes the technical wisdom that exists within it.
 
Joden / The advanced level of training
Ri ( discarding the kata)
Some practitioners of modern martial traditions dismiss kata and Shu-ha-ri as being too confining or old fashioned. In truth, this position is flawed because the purpose of kata is misinterpreted by them. Like so many arm chair experts, they have not been properly trained beyond the shoden level in kata and are commenting on a subject they simply are unqualified and therefore unable to comprehend. Like most observers outside the experience of deep study they see the kata as the art itself instead of a sophisticated teaching tool that is only a surface reflection of an arts core concepts. The kata, in their flawed interpretation "is" the art. This is like the flaw of assuming a dictionary to be a complete representation of language. Unfortunately numerous older martial traditions in Japan unintentionally reinforce this misinterpretation by overemphasizing the kata. Often with these schools significant core elements and knowledge have been lost to antiquity so that all that remains is the omote or outer shell of the kata.


Ri, What is it?
"Ri" is difficult to explain as it is not so much taught as it is arrived at. It is a state of execution that simply occurs after shu and ha have been internalized. It is the absorption of the kata to such an advanced level that the outer shell of the kata ceases to exist. Only the underlying truth of the kata remains. It is form without being conscious of form. It is intuitive expression of technique that is as efficient as the prearranged form but utterly spontaneous. Technique unbridled by the restriction of conscious thought processes result in an application of waza that is truly a moving meditation. For one who has achieved ri, observation becomes its own expression of reality. The mind is now free to operate on a distinctly higher level than previously possible. With ri, the lag time between observation and cognitive response is reduced to almost imperceptible levels. It is "ki". It is "mushin". It is "ju". It is all these things in combination. It is the manifestation of the highest level of martial ability.
The level of technical execution associated with ri is realistically beyond the ability of many practitioners. Most people are simply incapable of reaching this, the most advanced level of expression of a ryu's potential.