My understanding is that on a business hosting plan it is a dedicated (private) SSL certificate, along with a dedicated IP address (which the SSL needs). You would use with https://yoursite.com/
I would assume that you need to inform LP that you want to implement the SSL certificate, so that they can set it up properly for you (e.g., www or no www). I don't think it's automatically set up for you. Open a support ticket to talk with the techs about what you need to do.
LP also has free public SSL certificates, which you use with https://serverName.lunarpages.com/~AccountName/
. No setup is needed with that.