How Does

[bridgestreet]

a wi-fi connection work over the air?

[sunny-dave]

Well it could be magic ...

... or it could be http://en.wikipedia.org/wiki/Wireless_LAN

[bridgestreet]

But what actually physically connects them?
Everything must be connected physically in one term or another.
Be it through air or touch.

[sunny-dave]

Radio signals - which don't need air or touch.

[bibblebub]

electromagnetic waves do not require a physical medium such as air, they traverse vacua too

[bridgestreet]

Can you please explain that In English???????

[bridgestreet]

How do they convert from one end to the other?

[Tuvok]

Think of a radio. The signal gets transmitted and you receive it on your radio as it has an aerial.

Without getting too technical, radio waves are only one part of the spectrum. Light, infra-red, x-rays, ultra-violet and even microwaves are all "waves"

You mention a physical connection - there is no real physical connection - you get a suntan from sunlight, but you are not connected to the sun are you! It is the ultra-violet waves.