The Germanic sharp s (Scharfes s) or Eszet (literally S-Z) is a letter of the alphabet used only in Germany and Austria. Though ß is similar in appearance to an uppercase B and lowercase β, the letter is lowercase and has no uppercase form. Because it is never used at the beginning of a word, there is no real necessity.
The letter makes a similar sound to a double-s in German, though it sounds more like an sz combination in English phonetics. In fact, some of the rules for spelling have recently changed in Germany regarding the sharp s and more words are using a double-s instead of a ß. There are several rules and quite a few exceptions to those rules for how to spell a sharp s sound, which have prompted this change, because it causes confusion among people learning to write in German.
Spelling in Germany is referred to as orthodoxy. It is very strict and enforced by the government, that is, they set the standards. The spelling rules were originally established by the Staatlichen Orthographie-Konferenz (National Orthographic Conference) in 1901 and had an expiration date of August 1, 1998. In the few years prior to this expiration, Rechtschreibreform (spelling reform) caused quite a fuss in Germany. A judgment by the Bundesverfassungsgericht (German Supreme Court) had to be made to enforce the new rules.
Under the old rules (which are still applicable until July, 31 2005), one uses a ß over ss when the sharp s sound is at the end of a word, before a hard t, or after a long vowel or diphthong sound. For example, Wasser (short vowel), außen (long vowel), heißen (long diphthong), Fluß (end of the word), mußt (before a t). As always, there are exceptions. Also, German uses a lot of compound words. If a prefix word has a sharp s at the end, it used a ß. For example, Großschreiben is a compound word of groß and schreiben.
Under the new rules (effective August 1, 1998), one does not uses ß at the end of a word or before a t, only after a long vowel or diphthong sound. For example, musst (before a t), Flussschiffahrt (end of the word).