It's a good and valid phrase, meaning that you don't want to stick to what you have been doing for a long time. For example, after I turned 60, I started to learn French, to "broaden my horizon". And, I am going to Paris soon to practice it a bit.
Not at all. If you have been studying languages, and worked very hard, and then decide that you would also like to study mathematics, you are broadening your horizons. You are doing something different.