Why were Arthur and the other knights looking for the Holy Grail?

In most versions of the legend, the grail appeared to them in a vision (or possibly a miraculous appearance). After it vanished, they decided to seek it out; the reasons for so doing vary. For example, in Le Morte d'Arthur, the grail miraculously produces food and drink for the knights, and Gawaine states that he intends to find it at least partly so that he can get more food and drink. (On a less material note, he also says that he wants to get a better look at it.)