it depends on the individual doing the reading. generally speaking a person wants to have some sort of way to connect with the energy of the person they are doing the reading for. A picture is a useful tool because it provides a solid image to focus on.
Other options are a person's full given name and a general location (like city and state/country), or a personal item that has been worn regularly. Like a bracelet, pendant, or other personal article that could be borrowed for a while and then returned.
No, It is not at all important to give your picture to a Psychic teller. I have heard about many Psychic readers, they do your reading Online. Some are there which do your reading on Phone Calls. Even I have seen a Live example of my friend consulted a Psychic at http://www.martine-voyance.com/tarifs/, She was struggling from the problems of Stress, Depression. She was not able to come out of it. She tried antidepressants pills, but it has not even worked for some hours. Then someone told her to consult Martine Voyance. She consulted and it actually worked for her. Now, she is happy then before.