Yes, a "page" is made up of one or more modules, each allowing the page administrator to assign view or edit permission to one or more security roles or to individual users. Some of the newer modules also define custom permissions (such as the forum module which has custom permissions for post and moderate). So, for the announcements module, you would need to give edit permissions on that specific module to the roles or individual users you wanted to be able to create and edit announcements. Many third party modules and some of the DNN core modules also keep track of the "owner" of a particular item or record of information and can be configured to allow only the owner of that particular record to edit or delete it.

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Bill, WESNet Designs
Team Lead - DotNetNuke Gallery Module Project (Not Actively Being Developed)
Extensions Forge Projects . . .
Current: UserExport, ContentDeJour, ePrayer, DNN NewsTicker, By Invitation
Coming Soon: FRBO-For Rent By Owner