The information you share comes from your profile and your Updates. On the Settings page in your profile, you can specify who sees different areas, limiting viewing to "My Connections", "Anyone", or "Me Only". For areas that you set to "My Connections", you can also specify if your connections can share information about you that they can see with the applications they use, including applications developed outside of Yahoo! (third-party applications).
Let's say that you've noted your favorite bands in the Favorite Music box of the About Me section in your profile and this information can be viewed by "Anyone" or "My Connections", and let's say that you allow your connections to share this information with third-party applications. If one of your connections uses a third-party app (for instance, a music app), that app can access your favorite bands and recommend them to your connection. Now you and your connection have some music in common. You can chat about the music, listen to the same groups, and grab tickets together the next time one of those bands is in town.
If you want to opt out of allowing your connections to share your information with third-party applications, go to the Settings page of your profile and uncheck the box next to Allow my connections to share my information labeled “My Connections” with third-party applications they install and developers who made the applications.
Note: Third-party developers will not have access to the "Me Only" information that your connections would not normally see on your profile, even when checking this option.