When you agree to be monogamous, you promise your S.O. that you won't have sex with other people. This amounts to signing over some control over your body.
But how much?
This is a very tricky question for Mormons because the LDS church has taught that masturbation is a sin. So it's common for Mormons to think that marriage only makes it OK to have sex with your spouse, and any deliberate solo sex is cheating.
I think that attitude isn't conducive to a healthy marriage. It's not realistic to expect your rhythm and schedule to match up with your spouse's throughout your life, and whenever they don't match up, the result isn't fair to either spouse: the one shouldn't have to feel pressured to be available 24/7, and the other shouldn't be made to feel like his/her needs are irrelevant or that any impatience in getting them fulfilled is just selfishness.
On the other hand, I don't want to dismiss worries about masturbation as completely stupid. If your rhythms never seem to match up, it can be a symptom of a problem in your relationship. Additionally, I think there's a very real gray area on the question of cheating. Of course it makes sense to grant your spouse bodily autonomy (allowing him/her control over his/her own bodily functions), yet granting your spouse 100% bodily autonomy (saying anything goes) means allowing your spouse to be with other people. Some people are OK with non-monogamy, others aren't. If you don't believe me that there's a gray area, I've put up another new post at The Visitors' Center gleefully exploring the whole region. But if you've ever been monogamous and either you or your S.O. has ever been aroused by someone else, you know what I'm talking about. Precisely where do you draw the line?