The word oracle in Greek can mean several related things. It means a god who predicts the future, like Apollo. It also means the priest who hears the message, and the message itself, and the place where the priest hears the message. Most often it means the priest or the message.
The Greeks believed (like all other ancient people) that you could communicate with the gods at certain places, at certain times, through certain people, and that the gods would give you advice and maybe tell you what was going to happen in the future.
This is certainly no stupider than calling the Psychic Hotline, which thousands of people do every day. Actually, it probably makes more sense than that. First of all, both the Greek oracles and the Psychic Hotline have in common that they hear the same questions over and over, and they listen all day to people telling more or less the same kinds of stories over and over. "Will my boyfriend leave me?" "Will my kids turn out bad?" "Will I get this job?" After you have some experience, you can predict pretty well what will happen just because you have already seen the same thing happen to so many other people.
But the Greek oracles had a couple of advantages too. First, you didn't just come and ask your question. You had to hang around the temple for a while, talking to the priests, so they could get to know you. And they could see you, not just hear your voice on the telephone. Second, everybody came to the same few oracles for help, and the priests at these oracles (unlike the Psychic Hotline) compared notes with each other. So if you asked "Should I get married?" and the oracle said "Yes," and then next week your girlfriend comes and she asks, "Will Gorgias ask me to marry him?" then the oracle already knows the answer to that one. There is every reason to think that the oracles were worth the money they charged.
The most important Greek oracle was the oracle of Apollo at Delphi, though there were many others.
To find out more about oracles, check out these books on Amazon or at your local library:
The Delphic Oracle: Its Responses and Operations, by Joseph Fontenrose (reprinted 1981). For some reason there isn't any recent book on Delphi, that I know of.
Greek Religion, by Walter Burkert (reprinted 1987). By a leading expert, for adults. He has sections on each of the Greek gods, and discusses their deeper meanings, and their function in Greek society.