Firstly, the lady "floating" over the land is dressed in pure white. This may imply that she is an angel sent from God. This shows that Gast didn't take America's expansion for granted. He was saying that it was God that America owed its powerfulness to. The book that she is holding may be a bible, also showing America's trust in God.
To the left of the lady, everything is old and dull -- people are traveling in old wagons, on horses and by foot. To the right of her, where she has already passed, everything is industrialized. The old wagons turn into stagecoaches and the horses and people who are walking turn into trains. Also, you can see a bridge and a big city on an island (possibly New York City and the Brooklyn Bridge). This shows that as America goes further west and becomes a bigger nation, technology will grow along with it and because of it.
In her hand as she passes, the lady is running a telegram wire across the land. This is because new cities built in the west need a way to communicate with the rest of the nation, emphasizing both the growth of the nation and technology. Gast was very proud of the fact that America was becoming such an industrialized nation. He may have also wanted to show it off to other countries (this fact applies for the whole painting).
Americans, and especially Gast, were very proud of their growing nation during this time of great nationalism and expressed it any way they could to show it