This is a great question. The First Great Awakening was largely a spiritual movement that dealt with salvation from a Calvinist point of view. Jonathan Edward's sermon, Sinner in the Hands of an Angry God is emblematic of the types of messages during the First Great Awakening.
The Second Great Awakening was different in nature. It not only forcused on the spiritual elements, but what eclipsed this spiritual focus, to a certain extent, was the social element. Charles Finney and others preached a social gospel as well, that is, a gospel that sought to transform society.
Part of the reason for this was the theological emphasis of this movement. The Second Great Awakening moved away from a Calvinistic framework and embraced an Arminian theological outlook, which was more optimistic of human nature and social change.
Hence, closely allied with the Second Great Awakening was the prohibition movements, the women's suffrage movements, and the abolition of slavery, and a whole host of other social initiative. We can say that the social gospel movement was a natural outflow of the Second Great Awakening.