You have it about right. MagicJack must be plugged into a computer which is connected to the internet by some kind of broadband connection. Your cable modem and wireless router would be fine.
If your computer is not turned on, calls will go to a personal voicemail box which is included as part of your MagicJack service. If can check your voicemail from your MagicJack or from any telephone, cellphone, etc. The MagicJack service also will automatically email any un-retrieved voicemail messages to you as audio files.
[Moderator snip]So, if you're at home (or anywhere else) with your computer, you need to have it turned on to receive incoming calls. But when you're not home and/or do not have your computer turned on, your calls will be answered by voicemail.
If you want, you also have the option to set up call forwarding so that your calls will be forwarded to another North American number such as your cellphone or office phone. This feature can be turned on and off by logging into your MagicJack account from any web browser -- so even if you're away from home and decide you'd like to get calls forwarded for a while and then change back to letting voice mail answer for you, you can do so easily.
Hope this information helps.
Regards, Will