Nine ships of the Royal Navy have had this name. The most famous Beagle was a Cherokee Class 10-gun brig-sloop. Fully loaded it displaced almost 300 tons, was about 150 feet long with two masts, and could hold about 90 crew members. It was launched in 1820, commissioned in 1825 and sold for scrap in 1870.
The ship is famous because during its second survey mission (1831-1836, captained by Robert FitzRoy) around South America and the Galapagos Islands, it carried a young naturalist named Charles Darwin. The voyage showed Darwin a range of habitats and corresponding wildlife - the impetus for Darwin coming up with his theory of evolution (see also The Voyage Of The Beagle).
Source: Thomson, K. S. (1995). HMS Beagle: the story of Darwin's ship. New York: W.W. Norton.