Well, the truth of the matter is that if you wear ties, you will be hard pressed to escape wearing one. But woven material has stood the test of time for many reasons.
Weaving is accomplished by laying long threads lengthwise (warp) and interlacing threads across the taught lines. This creates woven fabric. There are three different types of weaves, plain, satin, and twill. Your woven necktie will most likely be a satin weave, or perhaps a plain weave.
The satin weave is most popular for ties, because it creates a shiny and lustrous fabric that is particularly beautiful when made with silk. A silk Satin Tie will reflect light naturally and have an almost three dimensional appearance. Cotton can also be used in a satin weave but it will appear less shiny.
The weave will be far hardier, and can have a lovely rustic look when combined with a material like wool. Woven neckties have more body and appear fuller than a Knit Tie, and have always been considered a classic. The knit tie on the other hand has only made a recent comeback to the professional man's fashion scene.
When matching a woven necktie to your dress shirt and suit pay attention to color and pattern first. Make sure these two issues are resolved before even considering weave. More on Matching Tie and Shirt.
It is important to match types of weaving with your suit and tie. Say you are wearing a brown tweed suit for example. This type of suit is a little more rustic, with an air of country chic about it, so you would be better off going with a plain weave tie in a cotton or wool to compliment the suit.
Or, say you really like your fine weave black wool suit. This type of outfit would look much better with a bold, satin weave tie.
If you are in need of more ties for your wardrobe, practically every menswear store on the planet has woven neckties, but some have better selection than others.
I really enjoy the designer collections at Raffaelloties.com. Also TM Lewin and Charles Tyrwhitt have a wonderful in house line that is very inspiring. Keep your eye out for designs and colors that appeal to you, and then check back on that designer's collection from time to time. You never know when exciting new material will appear.
Now that you know more about your woven ties, I'm sure you'll appreciate all the intricate workings that go on in order to make your necktie. When you put on a tie in the morning, remember, it's not just an object spat out by a factory, it's a piece of fabric art.