Kata is the essential practice through which all the basic techniques were developed and applied. They are a series of pre-defined movements against a series of imaginary opponents. Movements are intended to be precise and replicated exactly by students, as they have been passed on from sensei to student for the last 100 years.
Note that there are minor variations of techniques and movements within the katas as taught by various schools and styles. Beginners need not be concerned with such variations at this time.
More examples can be found in our Kata forum.
Nevertheless, we do not recommend beginners start with these. Instead, we draw your attention to another series of kata that were added after Higaonna and Miyagi taught these.
Taikyoku Series Kata (for beginners)
In addition, white belts in the Yamaguchi Goju-Kai (from which my training was derived) begin their training with a series of katas, all with the same floor pattern, known as the Taikyoku series, to teach basic techniques, movements across the floor and turning. Created by Gichin Funakoshi (founder of Shotokan) and Gogen Yamaguchi (appointed by Chojun Miyagi to head of the Japanese arm of goju-ryu), these are a good place to start.
Taikyoku Jodan I & II
Taikyoku Chudan I & II
Taikyoku Gedan I & II
Taikyoku Kake Uke I & II
Taikyoku Mawashi Uke I & II
Links to these kata will be added later. In the meantime, you can see several of them demonstrated by this young man here: