In Cement
Sometimes holes are made to install fences in cement driveways or sidewalks, and between the time the hole is made and the fence is installed, it rains or there is water runoff that will accumulate in the hole itself. This standing water must be removed via siphon or towel, or you will have to wait until it evaporates.
In the Ground
When a fence post hole is made in the ground and standing water remains within it, it means something about the permeability of the ground itself---the ground will not allow the hole to drain. This means the hole is deep enough that it is mostly in clay or the ground is incredibly hard or already saturated with water. There's also a chance that there is water underground, just below the hole made for the fence post hole, and it is seeping up. If this is the case, it may not be the best place to build a fence in general, as the ground may be unstable.
Water Pipes
If a fence post hole is constantly filling and refilling with water regardless of rain or dry spells, and it is beside your house or in a residential area, there is a chance a pipe was damaged or broken when the fence post hole was made in the first place. You will have to figure out what pipe or water line you hit and dig it up to replace the section of pipe you damaged or destroyed. To ensure this doesn't happen in the first place, it is important to look at the blueprint plans of your property, as well as your neighbors' blueprint plans, so you can be sure nothing it broken when you are making fence post holes.