Wii Points are the converted form of Nintendo Points.  Nintendo Points can be bought in-store and online where they are then converted to Wii or DSi points at home.  Once converted, they can be used to purchase games for either console via the given device's shop channel.  For the Wii, you visit the Virtual Console, browse the selections and then make your purchase and begin playing.  There are games from all the major old school consoles and new content in the form of Nintendo Wii Ware for gamers to choose from.

Once you have purchased your Nintendo Points, then entered them into the Wii Shop Channel and converted them, you can begin making purchases immediately.  When your Wii Points are stored, you begin to browse through the different video games available.  They are separately into various categories, but the easiest way to browse games is via which console they are supported on.  For example, if you are looking for The Legend of Zelda: A Link to the Past, you know this is a Super Nintendo title.  You would browse through the Super Nintendo category to find it.  Once you find it, you click on Buy and the Wii will download a A Link to the Past to your Wii menu.  When it has finished download, you are able to begin playing it as long as you have a Classic Controller hooked up to your Wii Remote.

If you do not have any Nintendo Points on hand and do not want to make a run to the store, you can use your credit card to buy Wii Points instantly via the Wii Shop Channel.  Simply login, choose that you want to buy some Wii Points, enter your credit card information into the system and you will be making new purchases before you know it.  As long as you have a credit card, you can purchase Wii Points any time you want to make a buy on the Virtual Console.