This tower is the only remaining part of the City wall. The tower had 9 shooting holes, enabling good defense of the city. The city wall around Leiden originally had 33 of these towers. One identical one called "Bourgondie" was demolished in 1871. Both have probably been named after the ruling landlords Maria de Rijke van Bourgondie and her husband Maximilaan, Archduke and later emperor of Oostenrijk (Austria).
Source: http://erfgoed.leiden.nl/geschiedenis/monumenten/muurtoren-oostenrijk/ (Dutch)
Picture: http://erfgoed.leiden.nl/uploads/pics/Muurtoren_Oostenrijk_-_Lotte_Gielis.jpg (taken by Lotte Gielis)