Directing the eyes is process of guiding the viewers eyes through a shot. Why? To ensures they won’t miss any story relevant information. The guiding starts at the most important element and works its way down to the least important one. Getting the viewers eyes to look at the most important element has to happen within a split second. The shot might be already over if it takes to long to find what’s important and what isn’t.
By using visual contrast we can direct the viewers eyes.
Like in this example. Our eyes almost snap to this white dot.
A more complex shot might look like this:
Its impossible to tell where the viewers eye might go.
By adding visual contrast again even with a complex shot we can direct where the eyes go no matter if its top left corner(red dot), right (darker dot) or to the bottom middle(brighter dot) .
There are all sorts of different techniques in cinematography to achieve visual contrast like shown in the simplified examples above. Many of these methods which are covered at the following pages overlapping each other like its the case with depth and separation.
Examples of visual contrast:

dark actors, bright background, rails leading towards action

bright actor face, dark background

color contrast
Some other techniques of directing the eyes include the use of shallow depth of field although lighting doesn’t have a direct influence on it as well as eye trace which directs the eyes across multiple shots and which is covered here.