I assume you're a Mac Os X user, or something pretty similar. You need admin rights to install new software like Limewire with MacOsX, hence the prompt for a user name and password to prove you are an administrator. If you are confused by that, it probably means you aren't an administrator. Find out who your administrator is, make them a cup of coffee and ask them to type in their password so you can enjoy Limewire, though of course only for entirely legitimate and exclusively work-related purposes.
Hope that helps. Frankly I'm amazed to see a message I can answer.
easterhay