The cauldron is a commonly portrayed tool, although not all modern Witches have one. There is a great deal of history and tradition, both mundane and magickal associated with the cauldron and for modern day witches it is a vessel where magickal transformation happens. Everything from brewing of potions to burning of incense and a great many other uses.
A few examples cauldrons throughout history and in present day would be the Gundestrup cauldron found in Denmark and even the Olympic Flame which burns throughout the Olympic games. Origins and reasons for these cauldrons are largely debated, but the fact is that the Cauldron has always, and will always be a great symbol of power.
At one point in history every home would have had a cauldron. They were large, wide mouthed pots placed in the hearth of the home over a flame. These cauldrons were used mostly for cooking, however for those who practiced the magickal or medicinal arts these large pots were also used for their trade to mix up or cook any number of potions, ointments and whatnot... They were even used in a form of divination known as scrying, where they were filled with water and gazed upon in search of answers.
Today's Witches tend to see the cauldron as a symbol of the Feminine Divine. It's associated with the element of water and the west and has connections with reincarnation and rebirth. Modern Wicca and Paganism's views of the cauldron have been greatly impacted by the myths surrounding Cerridwen.
The cauldron is used for different purposes depending on the ritual. Because of this the cauldron should be cast iron or similar material to resist heat. In addition it should rest on three legs, to signify Wisdom, Inspiration and Rebirth or Transformation. And although it should have a wide mouth, it's mouth should be smaller than the largest part of the cauldron's belly, in order so that it should have no difficulty holding liquids, flames or other objects.
A lid is recommended, but not a necessity. If a lid fits tight enough it can be used to snuff out the flames from a fire. Depending on where you purchase your cauldron you may have options with and without a lid, and many different sizes I'm sure. As with any tool, find one that fits your needs and tastes. Larger cauldrons are very impractical for a solitary practitioner, and there are many smaller "alter top" versions available.
Many of the traditional uses of a cauldron have been replaced today by a simple pot on the stove, or a mirror in the case of scrying. Because of this, the cauldron isn't something that everyone will need or even choose to use. If you feel drawn to a cauldron, there is nothing wrong with having one, but there is no need to feel compelled to buy one!