There are several different methods of centering oneself before performing a tarot card reading, each of them valid: meditation, a moment of silence, prayer, or even taking a moment to focus on the breath can help to provide the ambience you want when delving into the secrets of the cards.
The function of this behavior differs greatly depending on what you believe. For materialists, it can help to achieve a state of heightened awareness, remove the influence of negative thoughts, connect with the collective consciousness, and allow the mind to focus on what is directly in front of it; the reading.
For those of a more spiritual bent, it can also serve to connect one with a deity for guidance in the reading, or even to have the reading inspired by a spirit or spirits. Centering can also help to dispel evil forces and reduce internal chaos.