The simplest definition is that they are the part of the skin that contains the team color texture. There are more things you can do with them besides just team color, but I'm no skinner, so I don't know.
The alpha channel of a skin is an 'invisible' layer of the skin that controls where team colour goes and transparency. By editing alpha channels you can change the placement of team colour, and you can change how transparent a skin is. One of the best uses for alpha channel editing is that you can alpha out a skin's weapons, making models show weaponless in Warcraft III.
Do Icons require Alpha channels too? I hear you talking about skins and Alpha channels. So what you're saying is that an Alpha channel is an invisible selection in a skin that says where "team colour" goes? Am I correct following this?
Icons do need an alpha channel, but a blank one.
Yes, you are right in following, alpha channels show where the team colour goes, and they also let you add transparency (for ghost-style effects, or to completely erase something).