Who was or what is Týn in Prague?

As the English Wikipedia page says, "Týn" is the name of a nearby courtyard visited by merchants. Jonathan Reez points out that "Týn" itself is an archaic word for a fence. In this case, "before" probably means "in front of" (for example, as in "He appeared before the judge"), rather than "earlier in time than", though the church is actually older than the courtyard.

Wikipedia sources its claim about the name to a Czech web page which Google translates as (in part):

The most important religious building right bank of the Vltava is undoubtedly the Old Town church of Our Lady before Tyn, called the Tyn Church. Was named after the otýn?ného [I guess Google doesn't know how to translate that word] or fenced place, Tyn courtyard, which is also called Ungeld. This court has served since the mid-13th century, foreign merchants, who came here to spend the night and then paying duty. The church of the Virgin Mary is older, the former is mentioned together with a hospital 1135.

I'll add to David Richerby's answer. Translating from Czech Wikipedia, Týn (also Týnský dv?r, meaning "Týn Yard") was a fenced in and moated trader's yard where traders had to pay a toll ("Ungelt" in old German, which is also the alternative name) for protection.

I do not know about the meaning of the word Týn, but the fence explanation given by David Richerby sounds plausible. To me, as a native speaker, the word Týn doesn't really carry any meaning.

Finally, "p?ed Týnem" means "in front of Týn".