To "glorify" God has taken on an unfortunate twist in understanding in our time. For many Christians, to "glorify God" means that we do our best, put our best foot foward, spare no expense, etc., in regard to our work for God.
However, in the Bible I see a different idea. Whenever God's "glory" is mentioned, it relates to a physical, visible, sometimes audible manifestation of God Himself; e.g., God's glory was manifested in the column of smoke by day, fire by night, which led the nation of Israel through the wilderness; "the glory of the Lord" appeared in the temple to Isaiah, and was seen by Isaiah.
Essentially, man does not glorify God; God glorifies Himself. Or, to put it another way: a person glorifies God only when that person allows God to show Himself through him or her, so, what people see is not the person's best efforts on God's behalf, but they see God Himself, living out through the life and actions of the person. One glorifies God by denying oneself, which is what I believe Edwards is talking about. It's a subtle difference, but it's the difference between self-righteous behavior, and "death to self" which allows the life of Christ to shine through a person -- one is a "pretend" glory, and the other is the actual glory of God.