Hi Rudy,
I think you're looking for the Last announcements block, that can be added in the contexts 'Site home', 'Dashboard' and 'Course'. When you add the block to Site home or Dashboard, it only lists announcements accessible from there, but not from the courses the user is enrolled in (Or at least, I haven't found a way to make it do that).
Depending on your Moodle version and theme, there are a few other ways to display this information to your users. Most used is the Notifications icon available in the top bar of your Moodle, if you're using a Boost-based theme.
The course announcements forums have been set up to force subscription, which means all enrolled users will receive notification of posts there, via email or in-site notifications (or both).
The notifications box will display a row per post and will send the user directly to the corresponding forum when he/she clicks on it. Alternatively, the user receives the full text of the post in his/her email.