Strunz groupings are a means of classifying minerals, initially by the anion groups that they contain (these are groups such as sulfates, carbonates, phosphates, sulfides, etc.) The listing by Strunz groups allows one to drill down to the subgroups and see which minerals are closely related to them. You can also see the minerals in a Strunz group (subgroup) on the mineral display page. They are also accessible in the "Search" button from the navigation header.
The Strunz groups are named for Hugo Strunz who authored the 1941 book "Mineralogische Tabellen". His Mineralogical Tables have been through many modifications; the most recent edition, published in 2001, is the ninth (Mineralogical Tables by Hugo Strunz and the late Ernest H. Nickel (31 August 1925 – 18 July 2009)). James A. Ferraiolo was originally responsible for upkeeping it at Mindat.org and the IMA/CNMNC also supports the Nickel–Strunz database. There is a 10th edition in preparation, which is the one we should use when possible.