The salinum is a container for sacred purifying salt. The Romans and other ancient cultures considered salt to be a very powerful substance that removed negative spiritual influences. The Romans understood that salt had antiseptic qualities even though they did not know about bacteria, etc. Salt was used for health in baths as well as in medicine. The name of the goddess Salus (the goddess of public health) is associated with the Latin word for salt. Salt was also of course important for life itself, and was so precious in the ancient world that the Roman Legions were paid partially in salt.
A salinum for a lararium can be made of pottery or metal, and should have a covering so that the salt does not absorb moisture or get dirty. The salinum container may be plain or decorated as you choose. Sea salt or course granular salt is recommended, both can be found at any health food shop or in most grocery stores. Iodized table salt is less desirable as it is less traditional.