A pallet is a squat platform used to move small or delicate items in bulk quantities. By loading them onto the pallet, a large number of small items becomes one load, or delicate, heavy items can be moved by powerful but ungentle machinery such as forklifts.
A typical pallet is roughly four feet square by six inches tall and consists of a top and bottom surface supported by a minimum number of posts to ensure it won't collapse under load. Often the top and bottom are rough cut 1"x4" slats with wide gaps between the slats, and the support posts are little more than scrap wood of sufficient height. The sides are open to allow the forks of a forklift truck or a pallet jack to slide inside and lift the load (the forks should be perpendicular to the slats to allow maximum support). Most pallets are built as cheaply as possible, out of unsanded, unfinished, unpainted pine cut to a wide, almost haphazard tolerance. Since pallets are typically used only for shipping, the end customer usually doesn't see them so they don't have to look nice.
While the above describes a typical pallet, they are available in a wide variety of variations on the theme. Four by four feet is typical for most applications, but larger products require larger pallets and smaller loads don't need one so big. Pallets intended for extremely heavy loads are sometimes made of stronger (and more expensive) wood such as oak instead of pine.
However, as cost-trimming warehouse-style stores began saving money by simply setting pallets full of merchandise on the sales floor rather than paying employees to shelve them nicely, the roughly produced platforms became a liability. The warehouse employees that previously were the only ones to see the pallets could be required to wear steel-toed leather workboots, but customers balk at dress codes more restrictive than "No shirt, no shoes, no service." Open-toed sandals and unfinished protruding wooden slats are a recipe for a lawsuit, so plastic pallets have gained popularity due to their less dangerous smooth edges. Plastic pallets are molded as a single platform supported by pillars extending from the underside, and pose much less of a threat to unprotected feet. Areas where pallets are not exposed to the public still use wooden ones, because they are much cheaper.
Since there is no "standard" of any kind, pallets built by different manufacturers will be somewhat different (tighter or looser tolerances, taller support posts, different number of slats, varying gap width between the slats, etc). In fact, since the tolerances are so loose and the materials are often little better than scrap, two pallets built by the same manufacturer might look very different. This can make it difficult to design automatic pallet loading machinery, since the equipment must be designed to handle so many variations. Although manufacturers can tighten their tolerances for a customer on request, the result is more expensive and usually prohibits the customer from using pallets from other places. After all, when the receiving department brings in raw materials and spare parts, these are often on pallets themselves that could be re-used for free.
avalyn reminds me that pallets are often stolen for use as scrap wood. Since they're so cheap, they are often left outside overnight and become a tempting target for anyone who needs a bit of free rough lumber. I doubt anyone has ever been prosecuted for stealing a pallet left behind a loading dock due to their inexpense.