I have a Tomcat application. I have a public IP but I want to know how I can make it available on internet. Is it a network config or Tomcat config? I want to give a URL like www.somename.com and it should be able to redirect to my server ip and port for eg: 129.23.34.45:8080 on which my Tomcat is running.
That is a very general question. Please explain your setup. Are you self hosting it on your PC, or you have some sort of server. What OS do you use?
The general explanation would be to open the port on your firewall and put some kind of port forwarding on your router (port 80 to port 8080 would be expected). You can also change the port Tomcat is expecting connections from 8080 to 80, so you should only forward port 80 to port 80 on the inner network.
Here is a good explanation on how to reconfigure Tomcat:
http://www.mkyong.com/tomcat/how-to-change-tomcat-default-port/
Another thing you need is a domain name. You should find some that suits you and lease it for a period. After that you can bind it to your static ip address. You can do that at specialized providers such as GoDaddy, name.com or any other you get recommendations.
Here is how can you register a domain name:
http://www.thesitewizard.com/archive/registerdomain.shtml
This is the most general explanation you can get, not knowing your system setup or network setup. Of course, you should always consider just buying a hosting package with some hosting provider, depending on what kind of service are you providing.