I'm not familiar with the term "julienne" in cutting and knife skills. What is the purpose of it? How do I safely execute the cut?
Related question on applications of the cut: Julienne applications
The French have names for a lot of cuts, not just 'dice' and 'mince'. (and I don't mean 'large dice'). And that list is incomplete -- it's missing chiffonade ... I have no idea how many others.
Julienne is a cut where you have items looking like small sticks -- a few inches long (about 10 cm) , and about 1/8" (3mm) square.
It's also called 'matchstick cut' in English, if you don't want to use the loanword.
It's generally done with vegetables:
... and there are mandolines (food slicers) that can do this style of cut by just pushing the food through the blades.
As for purpose -- it's just one of many cuts that you can use to try to make sure that things are cut evenly. (especially when you might have more than one person doing food prep).
It's useful for trying to make sure that items cook (or pickle) quickly. It can also help make sure that harder vegetables (eg. carrots) are easier to eat (both to chew and to pick up with a fork). It can be used to otherwise change texture in a dish.
It can also be decorative if you cut up things of a contracting color (or colors) and sprinkle them on top -- bell peppers, carrots, apple, etc.)
I got the following definition and explanation from Wikipedia It is pretty clear and straight forward that I don't think I should add on my own explanations here.
Julienne, or allumette, is a culinary knife cut in which the food item is cut into long thin strips, similar to matchsticks. Common items to be julienned are carrots for carrots julienne, celery for céléris remoulade orpotatoes for Julienne Fries.
Trim the ends of the vegetable and the edges to make four straight sides. This makes it easier to produce a uniform cut. Trimmings can be used for stocks, soups, purees, etc. The measurement for julienne is ⅛ x ⅛ x 1 to 2 in (3 mm x 3 mm x 3 to 5 cm). Julienne usually applies to vegetables prepared in this way but it can also be applied to the preparation of meat or fish, especially in stir fry techniques. Once julienned, turning the subject 90 degrees and dicing finely (⅛ in or 3 mm) will produce brunoise (3 x 3 x 3 mm) .