The letter you are referring to is called a Long S, which was derived from the old Roman cursive medial s (an s in the middle of a word).

In many alphabets, some letters take different forms depending on their position within the word. English for example has capital letters which only appear in certain situations (beginning of sentences, proper nouns, abbreviations, etc). Hebrew and Arabic have final forms of certain letters, which only are used at the end of a word. the Greek letter sigma has three forms, capital, medial, and final.

The long s was used for a very long time, and can be seen in many ancient manuscripts. It eventually fell out of use in the 19th century, first being abandoned by printers and typewriters, and then falling out of handwriting shortly afterwards.