You cannot access the contents of an iCloud backup. The only thing you can do with a backup is use it to restore or setup an iOS device.
Other data via synced (rather than backed up) to iCloud via Settings > [username] > iCloud > (Contacts, Notes, iCloud Photo Library, etc) are accessed through the respective apps on the phone (e.g., the Contacts app, the Photos app, etc). The synced data can also be accessed by using a computer to log in to www.icloud.com.