The toast rack is a tool for serving toast, keeping the slices separated from each other.
Toast is made by heating bread. Heating the bread causes water dissolved in it to evaporate away, making the toast crispy and pleasant to eat.1 Toast coming out of a toaster is still warm, so evaporation continues until the toast cools down. If the water vapour cannot escape, it condenses on the surface of the toast, making it soggy and unpleasant. This is known as 'toast sweat'.
A toast rack stands one or more slices of toast upright, so that water vapour can escape from both surfaces of the toast. If toast is put on a plate, the water can only escape from the top surface, leaving the bottom surface to become soggy. If (god forbid) more than one slice of toast is stacked on a plate, every surface bar the topmost one will become soggy, as the water vapour being produced cannot escape.
If you're worried about the heat sinking properties of your toast rack, I suggest you purchase a plastic or ceramic one. Ceramic toast racks can be pre-heated so as to keep the toast warm.
Toast racks generally look like this:
##
##
toast --> ##
##
__ __ __ __ __ ## __
| | | | | | | | | | ## | |
| | | | | | | | | | ## | |
| | | | | | | | | | ## | | <- vanes hold toast upright
| | | | | | | | | | ## | |
| | | | | | | | | | ## | |
|\___|__|____|__|____|__|____|__|____|__|_##_|__|___/|
\____________________________________________________/ <- tray to catch crumbs
1 - That's not all there is to it - the heat of the toaster causes the sugars in the bread to begin to caramelise. This is what is responsible for the colour and flavour of the toast.