The thobe is a Saudi name for the traditional Middle-Eastern loose, long-sleeved, ankle-length shirt/robe which one pulls over the head to put on. (Various regions also have other names for the garment, such as "dishdasha," or jellabiyyah/djellaba.) Traditionally, the men's thobe is fairly plain, white in summer and darker colors in the winter, and made of linen or wool, though cotton and polyester blends are common now. (Martha Kirk's book Green Sands says modern men wear shorts underneath in summer; sirwal pants are more traditional. The Desert Boutique online store even sells long underwear which look just like those worn by Westerners to me.) Thobes often have pockets and can have various types of collars and cuffs.

Women's thobes are often heavily embroidered and made of more colorful fabrics; they can be sheer because the thobe is only an outer layer worn over a dara’a (a straight-cut dress) with sirwal pants below that. Women's prayer thobes are hooded, unlike the more everyday ones, and have hand slits rather than sleeves; prayer thobes are not intended to be worn outside. However, women's everyday thobes are covered with the abaya cloak when they leave their homes.

Sources:
Martha Kirk, Green Sands: My Five Years In The Saudi Desert, Lubbock, Texas: Texas Tech University Press, 1994.
http://www.saudinf.com/main/q031.htm
http://www.alhannah.com/index2.html
http://www.quickbizsites.com/desertboutique/home
http://www.arab.net/saudi/culture/sa_clothing.html
http://www.kfshrc.edu.sa/arabian/html/arabic_dress.html
http://www.ecssr.ac.ae/Land/costum.html
http://www.saudiembassy.net/publications/Magazine-Summer-01/Dress.htm