This question boils to the more basic idea of the smallest object that can be seen with a naked eye. For this calculation we need to make a bunch of assumptions to begin with.
The formula for the smallest visible dot size is:
p = 2 x d x tan(a/2)
p = smallest dot size
d = smallest focus-able distance for a human eye (in meters)
a = angular resolution (in radians)
At this point we would have to make bunch of assumptions so we could calculate the smallest viewable dot size or resolution of the naked eye.
An average adult's focus is limited at a distance of 10 centimeter or 0.1 meters. Similarly the angular resolution according to Wikipedia could be taken as one arc minute (1/60 of a degree or 0.00029 radians).
Therefore, p = 2 x 0.1 x tan(0.00029/2) = 0.000029 meters.
Thus the approximate resolution of a normal adult human eye should be around the 29 microns. As a comparison, human hair has an average thickness of around 100 microns.
It would also be prudent to mention that the resolution can differ from person to person depending on their vision health, age, etc. For example, a child has a much greater resolution than an adult due to the fact that their lens tissue is much more flexible at a young age and it can be used to bring objects much more clearly into focus at closer distances.
Note: There are no parameters available that can provide an an accurate equivalency of an human eye with a digital camera. This means that the resolution of an human eye cannot be provided in terms of digital camera (like pixel resolution). Any such data available on internet is only meant to communicate the complexity of the human eye and is derived by using multitudes of approximations.
Human Eye Resolution equal to 576 Megapixels
When the human eye is a digital camera, it turns out the eye has a resolution equivalent to 576 megapixels. It's just that, the eye is not like a camera with a single frame snapshot, but like a video stream. The eyes work tirelessly, moving quickly and update the image continuously to send it to the brain.