A knicker is a marble. A knickerbocker is a person who bakes clay marbles, i.e., a manufacturer of marbles. As is often the case, some of those knickerbockers took their job as their surname; just as we have Mr. Smith and Mr. Miller, we also have Mr. Knickerbocker. It is from this man that words like Knickers and Knickerbocker Glory arose. But as it happens the Mr. Knickerbocker that gave us so many familiar English words was, in fact, imaginary.
In 1809 Washington Irving wrote a book called History of New York from the Beginning of the World to the End of the Dutch Dynasty, which poked fun at the early Dutch settlers of Manhattan. As was his wont, Mr. Irving used a pen name, so this book was publicly authored by Diedrich Knickerbocker. (D. Knickerbocker was named after Mr. Irving's friend Herman Knickerbocker, but the book was not biographical.) This was a quite successful book, and Knickerbocker quickly became synonymous with the New York Dutch, and later, with New York and New Yorkers in general. (This is where we get the name for the basketball team New York Knicks, who are officially named the The New York Knickerbockers.)
The History of New York was illustrated by Robert Cruikshank, who drew the Dutchmen wearing knee-length trousers. This style of trousers also came to be known as knickerbockers. This style was popular all over Europe, and knickerbockers, and the shortened form knickers, became a popular term in England. Of course, these pants were common well before 1809, and were also called breeches, britches, breeks, knee-pants, plus fours, plus sixes, and a host of other names. So when the word knickers was borrowed by feminists as a 'polite' way to refer to an abbreviated form of pantaloons in the late 1880s, no one complained. These knickers were called 'bloomers' in America, and were indeed knickers, going down to the knee. They were still considered somewhat scandalous, even when kept well out-of-sight beneath the clothes. Today knickers refer to any type of panties (although if you are American you probably only know the word as appearing the phrase "don't get your knickers in a twist!"), while knickerbockers remain the term for short pants.
Oh, and for those of you who have to know EVERYTHING, the fabric that Webster1913 refers to below comes from the yarn that was popularized by 'knickerbocker suits'. Knickerbocker yarn is a type of rough-faced wool and cotton yarn that has fibers of various colors added into the mix. It is a type of flaked yarn.