Although it's usually thought of as a root vegetable - and looks like one -  celeriac isn't strictly the root of a plant but the swollen base of its leaf stems. To be exact it's a hypocotyl, the portion of stem found beneath the cotyledons (the seed leaves) but above the root.  It's a true celery, which instead of putting its energy into forming long stems, has grown a large bulb at their base. Celeriac differs from genuine root vegetables, which store a large amount of starch, in having only 5-6% starch by weight. 
Descended from wild celery, celeriac is by nature a marshland plant, requiring plentiful water and a long period of growth. In season from October to late February, it can be stored for three to four months in frost-free conditions. Young celeriac has a more pronounced sweet celery flavour; older bulbs can become woody in texture.
Celeriac preparation ideas at a glance:

Celeriac is very versatile and makes a wonderful mash, particularly when mixed with potato; creamed soup, gratin and slaw, which is how it is favoured by the French.  It has a corrugated surface which means that it traps the earth and needs washing well and peeling before use. The leaf stalks can be eaten like seakale, and have also been used as drinking straws in tomato-based drinks such as Bloody Mary. It's a good source of potassium and dietary fibre.
Always more popular on the Continent (where it's seen as a great accompaniment to fish and fungi) than in Britain, celeriac was introduced here in the 18th century, and came to prominence in World War 2 as a substitute for trenched celery, because it took less time and trouble to grow, and because every part of the plant could be put to use as poultry food.