Celery
Celery (céleri in French) is a highly versatile vegetable that is grown for its stems, root, leaves and seeds. Most common are the celery stalks or stems which are fibrous and stringy. The long stems make dicing easy since they are already thin and more-or-less evenly shaped.
Celery Root
Celery root, also known as celeriac in French, is not just the root of a bunch of celery. It is from the same family and tastes very much alike. Celery root is milder and (like other root vegetables) tastes more "earthy".
Chinese Celery is like the common variety of celery but it has thinner stalks and is stronger in flavour.

More on Celery
History
Celery is closely related to parsley and they exact history is difficult to study for that reason. Wild celery grew in the Mediterranean. In the Middle Ages, it was used as a diuretic, to heal wounds from animal bites, and to soothe nerves. Celery was quite bitter before it was bred in Italy to remove the bitterness.
The Secrets of the Seed: Vegetables, Fruits and Nuts by Barbara Friedlander p20
Ways To Cook
Celery is one of the three main components of mirepoix and therefore a staple in any kitchen. Similarly, it is also used for soffrito.
For elegant preparations, remove the strings from celery before cutting. (Then save the stings and peel for stocks!) The flesh of the celery is remarkably tender after removing the strings. On the flip side, the strings in celery is an excellent source of insoluble fibre.
Remember that celery leaves are edible and can make a lovely garnish but the taste is quite strong and can over-power other flavours. Especially the darker green leaves can be bitter and can taint the flavour of a stock, for example. The darker the celery stalks themselves, too!
Celery root (celeriac) is a fall root vegetable that can be roasted with other root vegetables, mashed like potatoes, diced for soups and stews and either shredded or cut into julienne for salads and cold dishes.
Celery salt is a common seasoning and is made from celery root. (Larousse Gastronomique, p 26)
Celery naturally contains a lot of sodium and is sometimes used to cure meats but can be misunderstood.