Irish dances are done to four types of music: jigs, reels, hornpipes, and set dances. The jig, which is generally in 6/8 time, has several variations, including the single (soft), double, treble, and slip jigs. Because they are relatively easy, single jigs are often the first dances taught; these are performed in soft shoes. The treble jig, in contrast, "has a slower tempo, but dancers triple the beats in hard shoes." Graceful slip jigs, which use a 9/8 tempo, are danced only by women and feature "light hopping, sliding, skipping and pointing." The reel, which originated in Scotland in the mid-18^th century, is a fairly fast dance in 4/4 time; it may be done in either soft or hard shoes. The hornpipe dates from the same era and also uses a 4/4 meter. Deriving from "English stage acts," it was originally a men’s hard-shoe dance but is now performed by both men and women. Finally, a set dance—done in hard shoes—"is performed to a specific tune which has remained set over time." (Haurin and Richens)

The focus of Irish dance is clearly on the foot work; the arms are held rigidly at the sides, fists closed. (The dramatic athleticism of Lord of the Dance's Michael Flatley, with his sweeping arms, represents a break with this tradition.) However, according to Don Haurin and Ann Richens of the Richens Academy of Irish Dancing in Ohio, "Previously [the hands] were sometimes more relaxed and were even placed on hips." Patricia Kennelly offered two possible explanations for this posture: first, she explained that these dances were once performed primarily by men, and that the straight arms might be said to mimic the rigid posture of soldiers going into battle. This seems a plausible explanation, especially since there is something in the dancers' high, light steps that is reminiscent of the marching steps of soldiers. Additional evidence might be found in the fact that in other parts of Europe—France, for example—what became "traditional" dances originated as exercises for military men. 

A second explanation for the rigid arms is also persuasive: the Catholic church frowned on dancing, and the straight arms somehow lessened their displeasure. "Some argue that stiff arms were less provocative, others argue that the church was trying to increase dancers’ self control" (Haurin and Richens). Similar strategies for circumventing the church's disapproval of dancing were practiced elsewhere. For example, in parts of French Canada Catholics practiced so-called "chair dancing," in which the dancers remained firmly in their seats while they tapped out a lively rhythm on the floor with their feet. It is likely that both of these factors played a part in the development of this bodily aesthetic in Ireland.

Sources:

Haurin, Don, and Ann Richens. Irish Step Dancing: A Brief History

Irish Step-Dancing: A Living Tradition

A Brief Overview of Irish Dance

Shoes: The Kennelly School dancers perform in both "soft" ("light") and "hard" ("heavy") shoes. The latter create a distinctive tapping or clacking sound against the wooden floor. In addition to their built-up heels, hard shoes (see photo below) have soles thickened at the toe, which give them a knob-toed appearance. Changes in technology have transformed these shoes, adding hollow heels and fiberglass toes, which maximize their volume. Previously, dancers used nail heads and put coins between the sole and the tip of the toe to heighten the noise of their "clicks" (Haurin and Richens). The distinctive clatter of hard shoes is said to have influenced the development of tap-dancing in the United States.