Subsidiary rights are the the rights to use/sell the work in a format other than standard print form. They can include:
- audio books (may be covered in geographical rights)
- foreign language or sales (may be covered in geographical rights)
- serialization (newspaper, magazine)
- digests or abridgments
- anthology or other collections
- licensing into greeting cards, coloring books, characters, dolls, stuffed animals, t-shirts, lunch boxes, etc.
- movies, video games, board games
- special editions for book clubs, Braille, etc.
New subsidiary rights are popping up all the time. Your publisher will probably list as many as they can think of in the initial contract offer. The reason being, they want to control the quality of all products that will be associated with your book, and also because they want to make more money. Nothing wrong with either of those.
Whether or not you let them have these rights as part of the regular contract is up to you. Some publishers absolutely want all of them. Others will negotiate. Some won't ask for any.
What you need to look at in considering which subsidiary rights you allow them to have is:
1. How likely are they to exercise those rights?
2. How likely would it be that anyone else would want to buy these rights?
If your publisher is unlikely to option these rights themselves, you might want to keep them. Or if you don't care about certain rights, go ahead and give them up. You're not likely to get a better deal (as in, more money) by doing this, but your publisher may have contacts that would be difficult for you to make, and they might be able to sell the options on those rights.
If you do let your publisher have subsidiary rights, make sure your contract includes what and how and when you will be paid if they exercise and/or sell those rights. If they exercise those rights themselves, they will be covered by some sort of royalty payment. If they sell the rights to a third party, the proceeds are usually split on a percentage basis after expenses. I've seen everything from 80 publisher/20 author (which I would never agree to, if I were the author) to 50/50 (which is much more common).