© Denzil Green
Salt Pigs are a large version of a salt cellar. Their function, though, differs somewhat: they are meant for daily storage of salt in the kitchen, rather than fancy serving of it at the table.
They are roughly cylindrical or ovoid, looking somewhat like an old fashioned diver's helmet with a rounded top, a flat base, a knob at the top, and a wide (usually lipped) circular opening at one side.
The opening on the side provides quick access to the salt. The top and lipped opening keep dust and debris from settling in. Miraculously, bugs avoid the salt completely.
If you turn a classically designed Salt Pig on its side, to stand it on its opening, you'll see that it resembles the back half of a pig. More modern designs, such as those by Nigella, resemble a pig less, and are likely not to have the knob at the top.
Salt Pig sideways, on its opening
© Denzil Green
Note, though, that fine-grained salt that doesn't have anti-caking agents added may clump slightly on the surface in extremely humid weather if not used for a while, but a few pokes with a finger or spoon are sufficient to break that up when it occurs, which is extremely rare.
Salt Pigs come in different sizes, made of different material. Some are porcelain, some are made of pottery. Most come with carved wooden spoons that hold exactly 1/4 teaspoon of salt, which is handy for quick precise measurements for things such as bread machine recipes.
When you want salt for a dish you are cooking, you reach into the large opening on the Salt Pig, and grab out pinches of salt for cooking. Larger Salt Pigs, obviously, will have larger openings and so be easier to reach into. With smaller ones, you'll have to use the spoon, or tilt them to get the salt closer to the opening for your fingers.
Many people find that it is actually easier to control the quantity of salt being used when doing a pinch, rather than shaking from a shaker, and so use less salt, because they can see and feel exactly how much salt they are using.
Most people keep them on top of the stove, or on a counter nearby, for quick access, rather than storing them in a cupboard.
Many people also have several Salt Pigs, for different types of salt.
19th century models often had a loop handle as well as a knob at the top. , 
 Pottery & Porcelain Glossary in: L. G. G. Ramsey, F.S.A., ed. The Complete Color Encyclopedia of Antiques. Preface by Bevis Hillier, Editor of The Connoisseur. Compiled by The Connoisseur, London. New York: Hawthorn Books, Inc. 1962. Revised and Expanded Edition
 Salt Kits. Description in Stoke Museums catalogue, accession number 1952 P7. Retrieved January 2010 from http://www.stokemuseums.org.uk/collections/browse_collections/ceramics/slipware_collection/salt_kits/000433.html
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