This example in our collection (of which a detail is shown on the right) is of glazed white faience and features blue decoration in the form of acanthus leaves surrounding a hand with an eye set into the palm. It was purchased by the British Optical Association from a dealer in 1937 and based on the markings to its underside we can say that its provenance is believed to be from Talavera in Spain. It might actually have been relatively modern at the time of its acquisition.
Various theories have surrounded this jar. Could it have been intended to hold eye ointment or some other salve or ingredient for ocular medication? Or was it symbolic? There is something almost mystical about the eye in the hand. Others think there are resonances of Masonic imagery about it and that the positioning of the little finger is symbolic as well.
In fact there is an established historical tradition within medicine for this symbol. You'll find it, for example, to this day in the arms of the Royal College of Surgeons of Edinburgh. The hand is associated with the surgeon who, by cutting open the body, sees into the places that others never do. Sometimes, of course, the surgical opening is small and so the surgeon is seeing by feeling. Before key-hole surgery using optical aids this was the only non too-invasive way to perform many operations. The idea is that the skill of the surgeon and the knowledge he gains through the use of his hands gives him a greater insight. If the symbol means that, then the contents of the jar, if it was ever meant to have contents, could have been any drug that would be useful for healing the body and not necessarily anything to do with an ophthalmological procedure.
If you have any alternative theories then do let the curator know.