John G. answered 09/09/19
Historian Experienced in American History, Research
Defining the line between "modern" and "premodern" can be a tricky thing to do indeed. While I don't know the exact text you're reading, what we can do is look at what is meant by the "modern era" and how we can then apply this to your question.
Historically-speaking, the term "modern" does not mean "new," but rather refers to a period of time where things started to take the general shape that they do today: the rise of nationalism (as opposed to globalism, which is a postmodern/contemporary phenomenon) bringing about new ethnically-based states, industrialization and technological advancement that brings about many of the material goods that we know of today (e.g., trains, phones, mass telecommunication via the telephone and telegraph, etc.). We see trends such as urbanization, the mass production of food and material goods, and the growth of the global economy.
So how does this tie into colonial America? For starters, colonial America had exactly none of these; while trade and industry did exist, the economy depended a lot on farming (including lots of subsistence farming), and most manufactured goods were produced not in factories, but in small guild-style shops. Additionally, although we conceive of the US as the first modern attempt at a democracy, the colonial era -- and indeed, the early country -- in truth operated more as a traditional oligarchy/aristocracy run primarily by the landowners.
There's a lot more to it than this, but this is as best as I can give without reading exactly how your text defines it. Hope it at least helps point you in the right direction.