The purpose of the Close Up (CU) is primarily to see something more clearly. It is used to better communicate the emotional or the physical and to try to bring the character and the audience closer together.
Most CUs have no purpose or aim beyond this passive curiosity. They are, for want of a better word, flat. Below is an example of this flatness, Rebecca Romijn Stamos in Femme Fatale:
Sometimes, though, the CU can be more aggressive, striving to get under the subject's very skin, such as in Michael Mann's Miami Vice. Mann wields the camera like a scalpel, the intensity of the camera-work matching that of the protagonist's experiences.
This intensity does not necessarily derive from proximity at all, but from the colour and tone of the shot, the way in which we are invited to see.
In Kill Bill Volume 1, as The Bride is surrounded by the Crazy 88, the camera is crashes into extreme Close Up yet the frame is used not as a microscope but as blinkers. What is important is what we cannot see. Despite our closeness we are unable to partake in her experience. The scale of her challenge is only in our imagination.
The harsh and unforgiving scrutiny of the former and the excluding, blind gaze of the latter coalesce in the work of Belgian directors Jean-Pierre and Luc Dardenne. Long stretches of Rosetta are in hand-held, unstable CU and we rarely turn away from the eponymous heroine's face. We zero in on her internal world and yet at the same time are made aware of the cruelties of the outside world beyond our vision, the weight that pushes the frame in on her:
A CU can also place us in the position of an entirely different character not shown. We adopt his or her point of view. It is an extension of their gaze, a reaching out of the eyes, the heart or of both. This can be used to communicate all kinds of things: lust, sympathy or, as in Miami Vice, the state of fear as you're hypnotized deeper and deeper into the eyes of a marks-woman who wants you dead:
Even when the camera has moved physically towards its subject it may do so only to allow a greater space for that subject to inhabit. Silent films offered CUs as stages on which to shine. The big and bold characters became larger than life and the actors could exhibit their (theatrical) craft. Here is one such moment from The Goddess featuring Ruan Ling Yu:
Jean-Luc Godard, in his Close Ups, achieves something quite unique. His compositions have an almost invisible, unfelt presence. They afford space for the character's thoughts to seep out and for their spiritual depth to be revealed. Beautifully lit, they recall religious icons in their uninvolved simplicity.
The different roles and textures of Close Ups are subtle and too numerous to explore fully . Nevertheless I offer one more, from Patlabor 2 The Movie. Firstly, it is a CU used to exaggerate the features for comic effect. Secondly, the camera seems to function as a mirror, as the dog appears to be regarding his own depressing situation with a self-mocking, complaisant air.