The Tallit is the Jewish prayer shawl.
The Torah says that all four-cornered garments must have "tassles" attached on all four corners - Tzitzit - and there is a bracha (blessing) to be recited when putting on such a garment. As is common, to increase the chance to bless G-D, Orthodox Jewish men often wear a small undergarment like a vest, with 4 corners, and Tzitzit attached, every day, just so they can make the blessing. This garment is known as the "Tallit Katan" (Small Tallit), or sometimes just as the "Tzitzit".
The full Tallit, however, is a larger garment also worn by men only (although in non-Orthodox groups of Judaism, some women wear them too). It is worn for the morning prayer service every day, together with the evening service on Yom Kippur. On Tisha B'Av, the Tallit, along with the Tefillin, are worn in the afternoon service instead of the morning service.
In the Ashkenazi tradition, a man only has to start wearing a Tallit from his Wedding, whereas in the Sephardi tradition, a man starts from his Bar Mitzvah. However, in both traditions, children will often wear one once they start going to Synagogue. This is in line with the general view that although children who aren't Bar / Bat Mitzvah don't have to perform any commandments, they should still learn about them and practice them.
A Tallit is a large place of rectangular fabric, often cotton, wool or artificial fibre, which is often decorated with a simple black or blue striped pattern. However, it can be as ornate or as simple as you want. There are also Tallitot which are all white (usually with white stripes of a different style on a white background). These are worn on Rosh Hashanah and Yom Kippur, times when we are trying to be especially pure and close to G-D. See Kittel.
It is worn by first being placed around the body over the shoulders and down the back. The top is lifted over the head to cover the eyes and the blessing is recited. It is then removed from the head and then the front parts are folded up over the shoulders. Some people bring it back over their head at certain parts of the service.
The key thing is that it has 4 corners, and has the Tzitzit on each corner. It is put on before the start of the service while reciting the Bracha, and worn throughout the whole service.
Some Jews pronounce the word "Tallis" or "Tollis". The differences are related to whether they are Ashkenazi or Sephardi, and the different customs as to Hebrew pronounciation. The Hebrew word is always written the same.