Students of karate practice (among other things) prearranged forms called kata. The requirements for advancing in rank generally include learning and demonstating new kata.
The first kata we learn is called Taikyoku Shodan, and the second is Heian Shodan. The term Shodan in these cases means the first in a series. Taikyoku represents bridge or causeway, while Heian means peaceful mind. Other kata the beginner studies are Heian Nidan, Heian Sandan, etc. Many internet resources exist for researching kata, though one should be aware that kata of the same name may be very different in different styles. Historically there have been some name changes (such as switching the names of Heian Shodan and Heian Nidan to make the easier one come first), so you may notice that the Heian series corresponds closely to what other schools call the Pinan series. Often minor changes exist from one school to another. An frequent example is that several of our kata have cat stance where other schools may have back stance. A site for viewing kata videos is the following Shitokai kata page. I've noticed that their Heian Shodan is very different from ours, but the following page has a video that matches our kata as well as I can tell given the resolution: Shotokan Heian Shodan.
Kata list (under construction) and (roughly) when we begin practicing it :
Taikyoku Shodan (hachikyu)
Taikyoku Nidan (sichikyu)
Taikyoku Sandan (rokkyu)
Heian Shodan (sichikyu)
Heian Nidan (rokkyu)
Heian Sandan (gokyu)
Heian Yondan (yonkyu)
Heian Godan (sankyu)
Bassai Dai "Destroying the fortress" (nikyu)
Annanko "Light from the south" (shodan)