Gelatine or gelatin is an odourless, tasteless and colourless substance used for thickening. It's used in cookery for gelling foods, being found in many commercial products such as jams and jellies, ice cream, preserved fruits and meats, powdered milk, meringues, taffy, nougat, marshmallows and fondant; home cooks often use it in desserts such as panna cotta. In the non-food world it's utilized for a range of processes such as photography, waterproofing, and dyeing; it can be a culture medium for bacteriological research and a coating for capsules (gel caps) and microscopic slides. It's a base for ointment and pastes such as toothpaste, and as an emulsifying agent in spray. It is used for glue or size, say in applying gold leaf. Pretty useful stuff.
Thing about gelatine is that it's a protein - collagen - derived from animal bones, cartilage, tendons, hoofs, ligaments and other yucky tissues such as pig skin. That's why it didn't become popular until it was commercially available in the late 19th century; before this time people had to boil their own animal bits for ages to make their own. (If they were lucky they could get their hands on isinglass, gelatine made from fish air bladders, or carrageen, a seaweed product, but these were rare.)
These days gelatine is readily available in any grocery store. It is sold in granulated or leaf (sheet) form. Granulated gelatine may be sold in a bulk package or in envelopes, but be careful with those envelopes; the amount they actually contain may vary widely and doesn't often correspond to the amount listed on the package (1/4 ounce or 1 tblsp (15 ml, usually), and I advise you to measure it to be sure. Leaf gelatine is less common; it's sold in packages of paper-thin sheets, four of which equal 1/4 oz package. Both products must be soaked first in cold liquid (water or juice or whatever the recipe directs) - 5 minutes for granulated gelatine, until pliable but still in one piece for leaf (1 to 3 minutes). The granulated gelatine softens and swells, absorbing the liquid and becoming an elastic, transparent mass; the leaf gelatine doesn't become a mass, but does soften, after which it should be drained. Then it must be heated over low temperature, stirring frequently, till it's dissolved. This amount will gel 2 cups (480 ml) of liquid.
Because it's made from animals, gelatine is not suitable for vegetarians. Substitute agar or kudzu starch.