Rei-taisai is the common name of the most important reisai (regular festival) that is performed on a day associated with the shrine.
Reisai are classified as 'taisai' (grand festival) according to the rules of religious services stipulated by Jinja-Honcho (The Association of Shinto Shrines). Therefore, reisai are usually called rei-taisai. Their formal name is Taisaishikireisai (literally 'regular festival in the form of grand festival'). In some cases, a festival may be described as 'xxxx Shrine Reitaisai Festival' in information about the shrine but it only means a festival performed as reisai.
For instance, the reisai of Kashihara-jingu Shrine is called Kigensai and the reisai of Iwashimizu Hachimangu Shrine is called Iwashimizu-Sai Festival and the like, but the reisai of Tsurugaoka Hachiman-gu Shrine is called 'Reitaisai Festival.'
For more details, see the article on reisai.