What does it mean that Gatsby had committed himself to "the following of a grail?" How does it relate to his dream in general and Daisy's role in his dream?

When Gatsby met Daisy, he was careless regarding women, taking as many as he could and taking advantage of their innocence. However, when he met Daisy, he was blown away by her and he became determined to do everything he had to do to deserve and have her.

In early literature, a grail was a sought after object, often some sort of cup, that people chased for it's great importance. Many times, the search for this object would mean the embarking on a major quest in order to reach this objective.

Therefore, we can conclude on the fact that Gatsby considered Daisy to be his grail as he pursued her.