Your browser permits you to grant or withhold permission for applets that could give others access to your computer. You are responsible for deciding who can have access. There is always some risk that such applets could contain viruses that would destroy data or backdoors that would allow others to access the information on your computer.
The jIRC applet is a commercial application purchased from JPilot (http://www.jpilot.com). It is signed with a Thawte security certificate and a Microsoft Authenticode certificate. These certificates provide some assurance that the author of the code can be identified, thus making it less likely that the code will contain a virus.
This applet is labeled "high risk" because it allows read/write access. Such access is needed in order for the applet to create a socket to allow you to connect to the IRC server and to enable the server to identify you using identd.