Beijing 24 Tai Chi, also known as Simplified Tai Chi or Short Form Tai Chi, is a form of Tai Chi Chuan (Taijiquan) that was created by the Chinese Sports Committee in 1956. It was designed to be an easier-to-learn and shorter version of the traditional Yang-style Tai Chi, which can have over 100 movements.

The Beijing 24 form consists of 24 movements and takes around five to six minutes to perform. It includes a range of Tai Chi movements such as ward off, roll back, press, push, and single whip. It is often used as a form of exercise and meditation, and is popular with people of all ages due to its accessibility and health benefits.

The form is widely taught and practiced throughout the world, and is often used in competitions and demonstrations. It is considered a good introduction to Tai Chi for beginners, and can also be a useful practice for experienced practitioners looking to refine their technique or focus on the basics

Names of individual movements

1. Commencing (Qǐshì, 起势), Preparation, Beginning
2. Part the Wild Horse's Mane (Zuǒyòu Yěmǎ Fēnzōng, 左右野马分鬃), LEFT and RIGHT
3. White Crane Spreads Its Wings (Báihè Lìangchì, 白鹤亮翅), Stork/Crane Reveals Its Wings
4. Brush Knee and Step Forward (Zuǒyòu Lōuxī Àobù, 左右搂膝拗步), Brush Knee and Twist Step, LEFT and RIGHT
5. Playing the Lute (Shǒuhūi Pípā, 手挥琵琶), Strum the Lute, Play Guitar
6. Reverse Reeling Forearm (Zuǒyòu Dào juǎn gōng, 左右倒卷肱), Step Back and Repulse Monkey (Dǎo niǎn hóu 倒攆猴), LEFT and RIGHT
7. Left Grasp Sparrow's Tail (Zuǒ Lǎn Què Wěi, 左揽雀尾), Grasp the Bird's Tail
8. Right Grasp Sparrow's Tail (Yòu Lǎn què wěi, 右揽雀尾)
9. Single Whip (Dān biān, 单鞭)
10. Wave Hands Like Clouds (Yúnshǒu, 云手), Cloud Hands, Cloud Built Hands, Wave Hands in Clouds
11. Single Whip (Dān biān, 单鞭)
12.. High Pat on Horse (Gāo tàn mǎ, 高探马), Step Up to Examine Horse
13. Right Heel Kick (Yòu dēng jiǎo, 右蹬脚), Separate Right Foot, Kick with Right Foot
14. Strike to Ears with Both Fists (Shuāng fēng guàn ěr, 双峰贯耳)
15. Turn Body and Left Heel Kick (Zhuǎnshēn zuǒ dēngjiǎo, 转身左蹬脚)
16 Left Lower Body and Stand on One Leg (Zuǒ Xià shì dúlì, 左下势独立)
-Single Whip Squatting Down, Snake Creeps Down,
-Golden Rooster Stands on One Leg, Golden Bird Standing Alone
17. Right Lower Body and Stand on One Leg (Yòu Xià shì dúlì, 右下势独立)
18. Shuttle Back and Forth (Yòuzuǒ yùnǚ chuānsuō, 右左玉女穿梭), Fair Lady Works with Shuttles, (Walking Wood), Four Corners, RIGHT and LEFT
19. Needle at Sea Bottom (Hǎidǐ zhēn, 海底针)
20. Fan Through Back (Shǎn tōng bì, 闪通臂), Fan Penetrates Back
21. Turn Body, Deflect, Parry, and Punch (Zhuǎnshēn Bānlánchuí, 转身搬拦捶)
22.Apparent Close (Rúfēng shìbì, 如封似闭), Withdraw and Push, as if Closing a Door
23. Cross Hands (Shízìshǒu, 十字手)
24. Closing (Shōushì, 收势)

Here is another link with more details about the history of the form:  www.qi-journal.com/taijiquan-24-style