This word, like the one that precedes and those that follow in the Amidah begins with "ha," meaning "the."
Gadol is one of the more familiar words to those even mildly familiar with Hebrew. Most people would (accurately) translate it as "big." But "big" is a spatial term, mostly understood to mean "occupying a lot of space." Hagadol modifies ha'eil, God, and therefore makes no sense in its common meaning. God is not big; in fact God is both nowhere and everywhere – geography is an irrelevant term.
Instead, it helps to think of the word gadol as meaning "great." And by great, I mean not only "terrifically good," but also "awesome" in both its classical and colloquial senses. "Ha'eil hagadol" carries the same sense of "God is great" as the familiar Muslim declaration.
The root from which gadol comes also produces the word that means to raise children, meaning not so much to bring them from being small to being larger – that happens pretty much by itself as long as they are fed and watered regularly. Raising a child to be "gadol" means bringing that child to his or her full potential, full greatness, to the best of a parent's ability. To say God is "Ha'eil hagadol" is to say that God is the One who has reached the fullest possible potential.
Some people are parents in their own right and others bear their share of the communal responsibility to raise children. When we do so, bringing a child from "katan/k'tanah" to "gadol/g'dolah" involves maximizing the divine image in which they were created, the image of Ha'eil hagadol, the One who has reached the fullest possible potential.