To julienne something, usually vegetables, is to cut it into thin uniform strips or matchsticks.  A good example of something that has been cut into julienne are French Fries.  You may cut something into a large julienne like the fat sort of fries you get with fish and chips, or you can cut thin julienne like for shoestring potatoes. 

I will post more detailed directions as soon as I find someone to come take the picture while I do the cutting.  Keep watching.