In addition to basic techniques, the Heian kata are the first things a student of Shotokan karate-do learns. There are five Heian kata: Shodan, Nidan, Sandan, Yondan and Godan (first, second, etc.). It is usually thought that 'Heian' means 'Peaceful mind', and thus refers to the state of mind of one doing the kata. However, Rob Redmond has pointed out that 'Heian' simply means 'Peaceful' or even 'Basic' - neither of the characters used to write 'Heian' in Japanese means 'mind'. There is a theory that 'Peaceful' in the name of the kata refers to the fact that they all begin with a block. Rob Redmond has argued against this idea, since all the other Shotokan kata start with blocks as well (see his website, www.24fightingchickens.com). It is also a matter of interpretation whether a given technique is a block or an attack.
The first of the kata, Heian Shodan, is the simplest, and is usually performed in the first grading. The most advanced Heian kata, Heian Godan, is much more complex. It is more a matter of taste which kata one thinks is the most difficult to do, though. I personally like Heian Sandan. The kata now known as Heian Nidan was the first to be developed, and was originally the first one students had to learn. However, Sensei Funakoshi thought it was considerably harder to learn than what was then Heian Nidan, so he changed the names of the kata.
The Heian kata contain most of the basic techniques of Shotokan karate. It is thought that they were developed by Sensei Itosu in the early 20th century, but there is no certainty of this. According to the legend, they were originally used to teach karate to children in Okinawan schools. Before the introduction of the Heian kata, the children had been taught the Tekki kata, which are considerably more difficult. It is thought that the Heian kata are based on more advance kata such as Bassai Dai and Kanku Dai, which were deemed too difficult for beginners to learn.