Regular configure mode lets all users who have configure rights get into the box and make changes are there are no controls over how the changes get written when a commit is issued. Uncommited changes are retained in the candiate configuration upon exiting configuration mode.
Exclusive - only one user can be in configure mode at one time. So they control the configuration untl they exit configuration mode. Uncommited changes are flushed from the candidate configuration upon exiting configuration mode.
Private - mutliple users can be in configure mode at one time. The commit and rollback commands will act on changes that the individual user makes. So if user A makes changes to "system services" and user B makes changes to protocols OSPF - then if they issue a commit command only their changes will be moved into the production configuration. If user B starts also editing "system services" and issues a commit that second commit will fail with an error. At that time user B can issue a second commit to force an update.
As with exclusive uncommited changes are flushed from the candidate configuration upon exiting configuration mode.
Dynamic - this is a fairly new command - it applies only to configuring routing policy and within policy only for BGP. The concept is that the validation process is less extensive so the commit times are far less. Really only applies to very large scale configurations with 1000's and 1000's of lines of route policies.
Hope this helps!