Filet is a type of crochet lacework usually done in thread, where double crochet and chain stitches are used to create a binary pattern of empty and filled squares in a grid. These are generally made to form pictures or script with filled squares on a mesh background. The basic idea is a lot like ASCII art.
Filet crochet is extremely simple to do. You only need to know how to chain, which is the foundation of all crochet, and how to make a double crochet stitch (also easy, usually the third stitch you learn). It is time-consuming, but all fiber art is, and filet is probably the least time-consuming of all lacework.
So what do you with it? Whatever you want. Traditional filet items include decorative borders for shelves, edgings on pillowcases, tablecloths and runners, doilies, bookmarks and framed wall pieces that say "Home Sweet Home" and the like.
If you're feeling ambitious you can make beautiful curtains and bedspreads that blend the old-fashioned feeling of filet with whatever modern motifs you can think of. I've also seen art installations using filet portraits that create interesting textures of light and shadow. Like any medium, the limits are really up to the crafter.
Right now I'm working on a filet gryphon that will eventually be about nine square feet and 100,000 stitches. It's about half finished now, and I'm pretty sure that when it's finished it will be the middle frame of either a kitchen curtain or a bedspread.
Throughout the 19th century and the early 20th, women in the USA were absolutely nuts about filet because it was an easy way to work up durable, fancy-looking decorations for the home at a low cost, and they used it to decorate every item they could get their hands on. It hasn't been as popular in recent years, and I wouldn't want to fill up my house with its Victorian vibe, but it does make beautiful accent pieces and a nice way to dress up a table on special occasions.