An Shiduch is often thought of as an arranged marriage in Judaism. Close but no cigar. It's actually an arranged introduction.
The Shadchan keeps a list of young men and women (usually from the ultra orthodox community), with basic information about them, what they like doing and so on. She (I suppose there could be a male shadchan but all the ones I've heard of are female) then simply matches people up and gets them together.
Unlike an arranged marriage, though, there is no pressure to get married from this stage. The couple will usually go out on a few dates, and then decide whether the relationship is worth pursuing.
Update 26/May/2022: 18 years later this bit reads a bit naive to me. While there is technically no pressure, in some communities there definitely IS societal pressure. So not formally "arranged marriages" but often, for practical purposes, can be very close to one.
The word "Shiduch" is used in a number of contexts - "I'm going on a Shiduch" (I'm going on an arranged date), or perhaps "He's my Shiduch" (He's the one I've been set up with).
When the young couples go out on a Shiduch, they often go to places where they can talk, and where they won't be seen by friends. "Shiduch Spotting" is a favourite game to be played in the foyer of hotels in Jerusalem! Look out for young men dressed in a pristine suit, and young women wearing their mother's pearls!!!