When we say that the colonial economy and society were "maturing" we mean that they were becoming more like those of an established country and less like those of a colonial outpost. In both cases, we mean that they were coming to be more self-sufficient and diversified.
When an economy and a society are not "mature" they depend on others to a large degree. The economy might, for example, only produce a few kinds of goods with the rest needing to come from outside the country. The same would go for a society, which might rely on other countries to set the fashions and to be the source of everything that was "classy."
In both ways, the colonies were becoming more mature during the 1700s. They did not become completely mature, but they did move much further towards being self-sufficient and independent in economic and social terms.