The following was gathered from  http://www.taichifirst.com/taichiyang/taichi-24form.shtml

T’ai Chi Ch’uan: National 24 Form

Standard Simplified Taijiquan Version Consists of 24 Movements  — Bejing 1956

This 24 Short Form is a Simplified Tai Chi Form. It’s also called the Standard Beijing Taijiquan 24 Form,

 

Chinese National 24 Tai Ji Form 

The Beijing 24 form has many names including the 24 step form, the Peking form, simplified tai chi and even just the 24 postures.

This simplified tai chi form was created in 1956 by the National Physical Culture and Sports Commission of the People’s Republic of China as part of the drive to document and standardise Wushu training and introduce competition forms.

The Beijing 24 is aimed at the beginner and uses 24 representative moves from the Yang style. Although it has been simplified by reducing the repetition of moves and some of the more difficult kicks it contains the important and traditional characteristics and features of Yang style forms.

The short form enables beginners, old and young, to concentrate on, and appreciate, the essential principles of Tai Chi of effortless movement, relaxation and awareness of the mind and body as one.

Depending on how fast or slow you like to do your form the whole form takes between 4 and 8 minutes to do.

It is said to be the most popular tai chi form practiced today. And because of this you will be able to find lots of books, dvds and classes for you to enjoy.

History 24 Yang Taichi Form

The 24 Tai Chi Form was developed in 1956 by the National Physical Culture and Sports Commission of the People’s Republic of China. A standard form was need for the Tai Chi competitions.

The Standard Simplified Beijing 24 Taijiquan Form was based on the Yang Family style of Tai Chi Chuan. The Yang Style of Taijiquan was developed by Yang Lu Chan (1799-1872),. Yang Lu Chan learned the Chen Style T’ai Chi Ch’uan from Chen Chang Xing (1771-1853).

Eventually the grandson of Yang Lu Chan, Yang Cheng Fu (1883-1936) modified and popularized the Yang Style Taijiquan (1883-1936)

Movements of 24 Tai Chi Form

The 24 Taijiquan Form could be performed in 4 to 8 minutes.

The 24 Taijiquan Form eliminated some of the movements that are found in the Yang Style Taijiquan 108 long form such as the Sweeping Lotus Kick, Step Up to Seven Stars, Snake Darts out its Tongue, or Carry the Tiger to the Mountain.
The short 24 Taijiquan Form also greatly reduced the number of times that some movements are repeated in the Yang Style 108 long form such as Grasping the Sparrow’s Tail, Waving Hands Like Clouds, Left Ward Off, or Single Whip. The traditional Yang Style Taijiquan long form has 108 movements (postures or parts).

The Standard Simplified 24 Taijiquan Form, short form, could be taught fairly quickly to students of various ages in physical education programs. The brevity of the form appealed to students of all ages. The short form could be done by large groups of people in rows since the movement choreography is in straight lines.

The short form provided a standard form for use in some competitions. The new short form was less physically demanding than longer forms and other Tai Chi styles, and appealed to older beginners. It provided a good introduction to the basic elements of the Yang Family Taijiquan long form. When done properly, the short form can exemplify grace, beauty, and many fundamentals of the art. For these reasons, the Standard Simplified 24 Taijiquan Form has become quite popular and is now taught, practiced and played all over the world.

 Internal and External Chinese Martial Art systems

More than 300 different known martial arts styles are practiced in China. There are two Chinese Martial Art systems, the internal and the external systems. The internal system includes Tai Chi, Sheng-I and Pa-Qua styles. The emphasize stability and have limited jumps and kicks. The external system includes Shao Lin, Long Fist, Southern Fist, and other styles. They emphasize linear movements, breathing combined with sound, strength, speed and hard power impact contact, jumps, and kicks.

There are many different styles or families of Tai Chi Chuan. The five which are practiced most commonly today are the Yang, Chen, Wu , Sun, and Woo styles. All Tai Chi styles, however, are derived from the original Chen family style.

Some people believe that Tai Chi was developed by a Taoist Priest from a temple in China’s Wu Dong Mountains. It is said that he once observed a white crane preying on a snake, and mimiced their movements to create the unique Tai Chi martial art style.

Initially, Tai Chi was practiced as a fighting form, emphasizing strength, balance, flexibility, and speed. Through time it has evolved into a soft, slow, and gentle form of exercise which can be practiced by people of all ages.

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Another good source

Michael P Garofolo presents very good research at  the web site
  A Note to Readers from the egreenway.com web site: 
The Cloud Hands website has been online continuously since 2001.  In 2009, over 1,350,000 webpages (excluding graphics) were served to readers around the world from the Cloud Hands website.  …  Cloud Hands is a very well-established and stable website.  It provides  a good …starting point for … online research into Taijiquan and Qigong.  The Cloud Hands website is funded entirely by Green Way Research, with volunteer efforts by Michael P. Garofalo.