What does the number of exposures mean?
On practically all SONY cameras this is the number of times the shutter had to mechanically move in order to produce an image.
Why is the number of shutter actuations/movements important?
Everything that is mechanical will eventually break or malfunction.
Most camera manufacturers rate the shutters for a certain number of actuations (like 75.000, 100.000, 150.000 or even more with some pro grade models).
This means that as long as the number of shutter actuations is lower than this, the chance of failure is very small.
On newer models with an electronic shutter, this is no longer a problem as there can be no mechanical failure.
Why do I get two numbers?
On certain DSLTs and DSLRs (A55, A33, A560, A580) the shutter could mechanically move more than once to produce one image -
depending on the mode (live preview on DSLRs, panorama, HDR, etc ...)
The second, larger, number is the number of actual shutter movements and the first number is the number of finished images.
Why does my camera have 0 exposures? / Why doesn't the exposure number increase?
Newer SONY models have an option to turn on electronic shutter.
In this case the number of mechanical movements of the shutter does not increase.
Try turning the option off in the menu and see if this causes the number to change.