What is American kenpo?

American Kenpo Karate (/ˈkɛnpoʊ/), also known as American Kenpo and Kenpo Karate, translates roughly to 'law of the fist' is an updated system of martial arts based on modern-day street fighting that applies logic and practicality. It is characterized using quick and powerful strikes delivered from all of the body's natural weapons, powered by rapid stance transitions, called "shifting." Beginners are introduced to basic attack responses, which comprise a larger system taught through scripted scenarios, which allow instructors a platform to share concepts and principles Ed Parker emphasized in his teachings.
The purpose of training in this manner is to increase physical coordination and continuity with linear and circular motion. Each movement, when correctly executed, leads into the next, keeping one or more of an adversary's "dimensional zonez" of height, width, or depth in check - therefore limiting their ability to retaliate. Should the adversary not react as anticipated, the skilled Kenpo practitioner, it is argued, is able to seamlessly transition into an alternative and appropriate action, drawn spontaneously from the trained subconscious. 

HISTORY of Kenpo

The following is mostly an excerpt from liveabout.com, slightly re-arranged and with some additional information.
The martial arts have a long and storied history in China. However, it is near impossible to trace most style lineages completely. Though Kung Fu is regionally known as an all-encompassing name denoting the Chinese arts outside of the country, in China the original term was actually 'Ch'uan-fa.' Ch'uan means "fist" and fa means "law." So when the Chinese arts made it to Japan during the 1600s, the literal translation of fist (Ken) and law (Po) turned the name into Kenpo.
The original Chinese arts were influenced by all types of exchanges in Japan (Ryukyuan martial arts and Japanese martial arts). In 1920, a three-year-old Japanese-American boy named James Mitose was sent to Japan (from Hawaii), where he studied what Americans now call Kenpo-type fighting forms. Mitose returned to Japan on subsequent occasions and eventually began teaching what he called Kempo Jiu-Jitsu or Kenpo Jiu-Jitsu (pronunciations vary). William Kwai Sun Chow was one of Mitose's top students (second Shodan). Along with Thomas Young (Mitose's first Shodan), Chow helped him teach in Hawaii until around 1949.
The kind of Kenpo practiced by Mitose and the like was more of a linear style. However, Ed Parker, a judo shodan introduced to Kenpo by Frank Chow and trained under William Kwai Sun Chow, received training while working in the Coast Guard and attending Brigham Young University. In any case, Parker changed Kenpo's form to make it a more street-wise style. These changes morphed into a new kind of Kenpo that soon became known as American Kenpo. Later, Parker began to stress more circular, Chinese movements in his teachings. And since he never named a successor to his style, there are several offshoots of his (and Mitose's) Kenpo teachings today. 

CHARACTERISTICS OF KENPO

Kenpo is a style that emphasizes punches, kicks, and throws/standing locks. The original Kenpo that came to the United States from Mitose and Chow emphasized more linear or hard-line movements, whereas Parker's later derivation, usually termed American Kenpo, emphasized [a combination of hard-line and] Chinese circular movements. In general, the goal of Kenpo Karate is self-defense. It teaches practitioners to block the strikes of opponents if needed and then disable them quickly with powerful pinpoint strikes that are categorized into named techniques. Takedowns and standing joint locks are also part of the art. Though forms are taught at many Kenpo schools, the style is often defined by the 'hands-on' and flowing approach to self-defense. 

legacy OF KENPO

Sr. Grand Master Edmund Parker is the undisputed “Father” of American Kenpo Karate; adapted from his lessons from Mr. Chow. In 1956 Parker founded the International Kenpo Karate Association, which went on to worldwide renown. Parker taught martial arts to many actors and celebrities such as Elvis Presley and Steve McQueen. He also appeared in movies and television shows such as numerous “Pink Panther” films and “I Love Lucy.” Founded and codified by Mr. Parker, American Kenpo is primarily a self-defense combat system. Parker made significant modifications to the original art of Kenpo which he learned throughout his life, by introducing or changing principles, theories, and concepts of motion, as well as terminology. Parker further adapted the methods so that they would prove more practical real-world fighting scenarios. It is in this way that American Kenpo became more of a system than an art form. It is a system that, according to Parker’s wishes, continues to evolve today, although in splintered forms. Parker believed in tailoring Kenpo to the individual and would also encourage his students to explore the unknown areas of martial arts.
At the time of his passing in December 1990, Parker created 154 named (known by practitioners as 'ideal phase') technique sequences with 96 extensions (additional movements after the base technique), taught in three phases (Ideal, What-if, and Formulation Phases). Parker had created Short Form 1, Long Form 1, Short Form 2, Long Form 2, Short Form 3, Long Form 3, Long Form 4, Long Form 5 (Surprise Attacks), Long Form 6 (Bare Hands vs. Weapons), Long Form 7 (Twin Clubs), and Long Form 8 (Twin Knives). However, many schools rarely teach beyond Long Form 6 - preferring to defer to other martial arts for use of weapons. 
Mr. Parker wrote numerous books on the American Kenpo Karate System, the definitive being his Infinite Insights series. If you are interested in further reading, speak with the instructor about additional materials.