An application server is a host that provides one or more services over the network. Application servers can be "secure" or "insecure." A "secure" host is set up to require authentication from every client connecting to it. An "insecure" host will still provide Kerberos authentication, but will also allow unauthenticated clients to connect.
If you have Kerberos V5 installed on all of your client machines, MIT recommends that you make your hosts secure, to take advantage of the security that Kerberos authentication affords. However, if you have some clients that do not have Kerberos V5 installed, you can run an insecure server, and still take advantage of Kerberos V5's single sign-on capability.