This is an old kingdom mummy these are the only bone of the foot I have, cannot understand the cause of this polishing. Sadly the photo does not do it justice.
Eburnation is typically indicative of osteoarthritis. The aetiology of OA is multifactorial. Women are especially vulnerable to the condition post menopause due to the hormonal changes. It is also associated with load bearing joints - so perhaps this suggests strenuous physical activity on behalf of the individual, particularly through this area of the foot.
As for the actual polishing of the bone, it is caused by the breakdown and eventual loss of the cartilage of the joint. Osteoblasts then respond by depositing subchondral bone (sclerosis), which eventually leads to bone-to-bone contact. This produces the polished effect you can seen on the joint surface.
There are two factors in play the very flat proximal joints where would normally expect facets and also on first photograph development of osteophytes distally. Both indicating as stated by others signs of osteoarthritis. I think that the flat planes and subsequent eburnation could be due to flat feet. A quick look at the literature following up that idea shows a link between OA and flat feet, http://www.sciencedirect.com/science/article/pii/S1063458409003057.
Before I start my comment, my computer is preventing me from viewing your images, so I may be completely off-base here; eburnation can also result from non-union of fracture, no? However (based on the comments above mine) it sounds like the eburnation is located on the articular facets, so non-union of a fracture may not be the strongest diagnosis. The most likely cause, Osteoarthritis, has been noted several times. If it is in fact Osteoarthritis, I would look for various additional signs of osteoarthritis on other appendicular joints. From what I understand, the knee joints and pelvis are especially useful in this regard, as they are prone to suffering cartilage damage from both strenuous activities and ambulation. I'm fairly certain that STANDARDS FOR DATA COLLECTION FROM HUMAN SKELETAL REMAINS has a section devoted to osteoarthritis that is fairly useful. I apologize in advance for not providing you with the exact page numbers, but I'm currently traveling by train.
Here are a few sources that might aid you. :)
Rogers, J., and Waldron, T. 1995. A Field Guide to Joint Disease in Archaeology. John Wiley: New York.
Weiss, E. and Jurmain, R. 2007. Osteoarthritis Revisited: A Contemporary Review of Aetiology. International Journal of Osteoarchaeology. 17:437-450.
Ortner, D.J.2003. Identification of Pathological Conditions in Human Skeletal Remains. Academic Press. San Diego, CA.
Roberts, C., and Manchester, K.1997. The Archaeology of Disease. Cornell University Press. Ithaca, New York.
Mann, R.W. and Hunt, D.R. 2005.Photographic Regional Atlas of Bone Disease.2
nded. Thomas, C.C. Springfield, IL.
Jurmain, R.D. 1980. The pattern of involvement of appendicular degenerative joint disease. American Journal of Physical Anthropology. 53:143-50.
Parting note: David Bryson's hypothesis seems fairly strong.. I would investigate that idea, look for other signs of Osteoarthritis in the other appendicular joints (if there isn't any, the flat foot theory gains some additional merit), and then assess the Age at Death. If the individual died young (relative to a relevant demographic) and had no other sign of osteoarthitis, then Bryson is most likely correct.
I'd recommend consulting Tony Waldron's work on Degenerative Joint Disease as this appears to be osteoarthritis. Jurmain's recent summary of joint disease and attempts to link these to activity in "A Companion to Paleopathology" (edited by AL Grauer) may also be helpful. Without large trends by age, sex and other variables, it is hard to say what this might mean in terms of who does what kinds of labor, etc. in any population. As others have noted, this is because OA/DJD are multifactorial and age, sex, and genetics matter.
I've looked at both pictures and could not see the eburnation areas. Regarding their paleopathological meaning, several of the previous answers were correct and give you a very good starting point for the analysis of the lesions. But from those pictures, one cannot speculate further - such as, what type of movement was involved (given that you speak of eburnation)...