You need to be the owner of the shared folder in order to kick out a member. If you created the folder, you are the owner unless you've left the folder or transferred ownership to someone else. Owners of shared folders are marked "owner" in gray in the folder's settings on the Dropbox website.
When you kick members out, you'll be given the option to let them keep a copy of the shared folder and its files. If you choose not to, the files will be removed from the members' online accounts immediately and from their linked computers the next time they sync using the Dropbox desktop application. In this case the files will be permanently deleted from those accounts, meaning they can't be recovered even with Dropbox's restore feature.
If you allow kicked-out members to keep a copy of the shared folder, you might want to avoid confusion by letting them know that their copy will no longer sync with other accounts.