The root word is visible. This means that it can be seen or is able to be seen. Visibility is the state of being able to see or be seen. For example, "a reduction in police presence and visibility on the streets." It can also mean the distance one can see as determined by light and weather conditions. For example, "visibility was down to 15 yards". Lastly, it can also mean the degree to which something has attracted general attention. Using this definition, it is synonymous to the word prominence..
