Wat Phra Singh is not an unusual name for a Thai temple: wat means Buddhist temple, phra is used to refer to a Buddha image or a monk, while singh is a mythical lion-like animal. The most famous Wat Phra Singh in Thailand is probably the one in the city of Chiang Mai, built inside the old city walls at a time when Chiang Mai was the capital of the northern Thai kingdom Lanna or Lan Na. The wat was originally built in 1345, at which time it may have simply been a stupa erected by a king (and descendant of the great Mangrai) to honour his father. The stupa still stands, but most of the buildings you see on the site today are of much more recent vintage. The teak temple is a beautiful example of Lanna or northern Thai architecture, with soaring "wings" on the ends of the eaves and lavish carved wood and stucco decoration throughout. The walls inside the temple are adorned with paintings depicting Lanna life in the 19th century.
Originally called Wat Li Chiang Phra, the name was changed to Wat Phra Singh when the Phra Singh Buddha image was first housed there in 1367. According to legend, the original Phra Singh image was cast in gold in 360 AD in Ceylon, now Sri Lanka, and somehow made its way to Siam. As the style of the image is early Siamese, most scholars consider this story to be fanciful at best. In any case, the image in the temple today is a copy; the real one is in the museum in Chiang Mai.
See photos of the various buildings on the grounds, and a brief history, at
http://www.age.ne.jp/x/botravel/html/cmg/singh.htm
And if you ever find yourself in Chiang Mai, visit this temple. It's beautiful and, being right inside the city, very accessible.