WIFI. What can it be used for?

[MesterLars]

I've never really used any wireless components, so I think I need some basic understanding of the concepts.

My rooter is with cable (for now)
My cellphone doesn't have bluetooth (for now)

So what can a MB with WIFI be used for? (e.g. the Asus P5B WIFI Deuxe) ?

1) Is it just to connect to your wireless router?

2) If not what is it then? And Is it of any use without a wireless router?

3) Does it function while the computer is off? (I guess not, but you'll never know these days)

In the future I might acquire some devices like Squeezebox and Lego Mindstorm or wireless gamepads.

Can a WIFI Motherboard be helpful with those?

As you can see I'm a little lost and that is preventing me from upgrading my computer at the moment, because I fear I might miss out on something

 

[infornography42]

You can connect wireless devices without a wireless access point (wifi router) using what is called Ad-Hoc mode.

Mostly wireless networking is just there for convenience and a minimum of cable mess.

I generally prefer to use cables for extra speed and reliability (not that wireless is unreliable, just less reliable).