When you make a client inactive in Contacts, they can still log into Realm, perform searches, and send you a message (if they created an account to use REALM). It is also used to organize your contact list, keeping clients you are actively working with in one list and ones you're not working with in another.
When you disable a client, they will no longer be able to log in; if they attempt to log in, the message returned is “Your sign-in can’t be completed at this time”. (This is for clients who have created an account to use REALM)