Campaigns are very very useful, and can be used for all sorts of things. Basically they are a way of grouping contacts together.
If a user is a System Administrator (or any profile) and can see but not edit campaigns, then you need to check the Marketing User checkbox on their User profile.
Make sure you enable Feed Tracking on Campaigns
And vote for this idea to enable Feed Layouts on Campaigns https://success.salesforce.com/ideaView?id=08730000000l966AAA except for the fact that it will never happen because of The Lightning Experience now.