Yes, I borrowed that quote in the title from Primeval because I've been going through a rewatch of that wonderful show and that quote just kind of wandered into mind as I started contemplating something: the Reader, specifically the Reader faced with a great body of reading material that will never come to an end.
We tend to go through phases in what we enjoy reading because there are so many possible things for us to read. To start with, there are centuries' worth in books and other material. You start off reading the main titles, only to realize that there are other, smaller (that is, less well-known in the present day) titles that you now want to read, as well. Like if you start off reading Jane Eyre and end up reading Agnes Grey or start with Pride and Prejudice and move on to Pamela and Anti-Pamela and The Victim of Prejudice. Things like that: the more books you read, the more books you feel like you need to read. For all that the writers are long gone, your quest is as new as if these are newly-released titles. This is connecting with the Past.
Connecting with the Present is easy to picture. You go into a bookstore and see a New Release that looks good and you buy it. Or you go in to get a new book by an author you've previously enjoyed reading. The Present is alive and tangible, constantly moving, and it directly references the time in which you, the Reader, live. Even if the setting isn't present day, certain traits of style or theme tend to give away a book's written era.
And the Future? Well, apart from people reading advanced reader copies of books that will be published in the future, I'm referring to this: those books that you expect people will still read or remember in the years to come. Some books get remembered simply for their popularity (some of the "classics" that we read aren't necessarily highly literary--they're just good reads, for people of their eras and for people today). Some for their connection to politics, history, or maybe social commentary (think Uncle Tom's Cabin or The Jungle). Some are simply stunning pieces of artwork. Sometimes we can't tell what books the future will hold onto, even if there are some that we think should be remembered. But sometimes we can be pretty sure. Books like this usually match at least two of the three points above and they are much talked about. Journalists as well as critics reference them, and college classes start adding them to the curriculum despite how "new" they are. Reading these books feels like glimpsing the future--glimpsing how people later on will view our present.
I am the Past, the Present, and the Future. A book really can take you anywhere.