Read-only access to CiviCRM
You didn't specify which CMS you're using but between your CMS permissioning and Civi ACLs, that should be possible.  See here for some info: http://book.civicrm.org/user/initial-set-up/permissions-and-access-control/

Just a thought to consider though... if you want to present particular sets of data to your board members in a simplified way, creating Views (if you're using Drupal) or similar presentations might be a viable alternative.  Sometimes the back-end, administrative angle of Civi can be a bit confusing for folks who don't use it regularly, particularly if they're not very technical.

Hope this helps,
Lesley