This is a stand for Saligrama, an aniconic representation of Vishnu. Technically it is ammonite fossils from Gandaki River, Nepal. To Vaishnavites, Shaligram is more pious than the consecrated Vigrahas.
“The Lord resides in many places in which he may be worshipped, but of all the places Salagrama is the best – Garuda Purana”.
The four pegs support a tortoise, an inverted lotus, a coiled five-hooded serpent (Possibly Ananta). On the sides, there are two peacocks. The religious significance of peacocks, in this situation, is not known.
The coiled serpent creates a cavity and that cavity will support the Saligrama.
The usage of such stands is as in the picture. It is from Anantapadmanabhaswamy temple, Trivandrum. Thanks to Twitter (Nikunj Shah) for the picture.
This stand looks to have been used, see the wear on the tortoise. This stand may not date earlier than the nineteenth century. The stand is about 10 cm in height and, most probably, it is from South India. This blogsite has some more examples of Saligrama stands and those are from the Eastern parts of India, Garuda stand.
2 Feb 2020: This is also known as Sesha Peetha. Sesha and Anantha refer to the snake on which Vishnu rests. Thanks to Karthik, FB comment.