Reading widely helps you get a lot more out of the books that you do read. You are able to understand the context, the allusions, the vocabulary, the things that are being suggested more subtly, the themes, etc. Just being told about the Great Depression at the time of reading Of Mice and Men, but not really ever having heard about it before, not realising what life might have been like, having no idea about what the American Dream represented etc, makes it harder to really understand the book. But if you've read various other books set around the time, even children's books, you just have a sense of what the world was like.
Or trying to explain some poetry to a pupil, as I was a few months ago, when she didn't really have an idea of the degree to which sex outside/before marriage might have been disapproved of, or why; another had little idea of how important religion was, or the role of women, etc. so all of that had to be explained before the poems would make much sense.
Many of the children I worked with hadn't heard of the British empire, for example. Or had little idea when Darwin and his ideas were becoming well known, etc., etc. So when reading books that had themes of science/religion in, much of it went over their heads; similarly about articles and stories written from former colonies - the pupils didn't really get that their perspective might have been ignored for years, that some of the books/poetry had unconscious bias to it. They knew little about the first world war and what life might have been like before it.
But a lot of that broader experience can be gained from many other books, children's books, films, etc. I learned a lot of historical type things from a diary series of children's books written by well known children's authors, each taking a different historical time period, and writing from the view of a child at the time. And there are tons of historical children's books that don't have the history as the main subject, but are just set in that time period, and you can absorb so much general stuff about the time as a result. (No, not always perfectly accurate, but a whole lot more accurate that some of the misconceptions that 15 year olds might have otherwise!). You also get an idea of language, how words have changed, famous sayings and proverbs, how words are used differently in other times and places, and so on.