Imaging systems aren't made of just optical elements. To generate an image, we also need a sensor. In many optical systems, this sensor is a digital camera device, typically based on either CCD or CMOS technology, where the light is projected on a grid of individual light sensors we call pixels ("pixel" is a contraction of picture element). In laser scanning confocal we use a single light sensor and scan the sample using a laser then measure the light emission at regular intervals.

In either case, the light coming from the sample is not measured in a continuous fashion, but at specific intervals. The separation between those measurements is what we call the sampling resolution. 

Because of this, the ability to resolve objects from an image isn't limited by the optics alone, it is also limited by the sampling frequency. If the inter-pixel separation is equivalent to 1um when we project light from the sample onto the sensor, the smallest gap we can measure will be larger than this since we need at least 1 pixel of separation to know a gap exists reliably. Likewise, if we are looking for fine features of 1um width in the sample, we really need a sampling frequency of at least half of that. In camera systems, the sampling frequency is the pixel separation on the silicon in the sensor / overall magnification of the optics. This number also serves as a calibration for the size of features in the image. A 10x lens paired to a camera with 5um pixel separation has a sampling resolution of 0.5um.

In this example above, the image on the left is under-sampled. It means that we cannot reliably say whether this is one continuous object, or two distinct objects that are in close proximity. 

The image on the right is over-sampled. We can see the gap between the two objects, but the pixels are so fine that we have a lot more data to process, without getting any valuable information that might allow us to make significantly better measurements of the separation in the image.

The image in the middle is a good compromise between having the ability to still see the gap between the objects, with at least 2 pixels separating them, but without collecting so much information that we put an unnecessary burden on our computer to store and process the data.