The IRC server wants to ask an ident server on your system which user really is at the network port you are coming from. This is a feature which is very useful for IRC server administrators when talking to systems on which a lot of users login. This way, it's easier to pin-point a user on the remote system in case of abuse.
To arrange that the IRC server can ask your system who is connecting, your system must run an ident server on port 113. This is what the Java applet is trying to do: startup such a server. However, the security settings of the system you're on deny port 113 from being opened by you. It might be that you're a regular user on a UNIX system (there I'm sure that normal users may not open network server sockets below port 1024). If you're not an admin on the system, I don't think you can startup the connection from there.
