There are a number of spells known by this name. All of them have the same basic affect: The movement of people and/or objects from one plane to another. These spells must be cast at a portal or they do not work at all.
Fundamentally, Transport spells are very similar to Teleport, though they are generally easier. Many of the complications of Teleport have been demonstrated to be handled for the wizard by the portal itself (clearing objects out of the way, etc). The varieties of the spell arise from trying to make the spell more comfortable. For reasons still unknown, the standard teleport spells on which Transport are based produce varying levels of discomfort among people being carried through a portal. Most wizards can learn the easiest form of the spell which produces levels of discomfort that can easily be described as "extremely painful". A notable exception is the mass transport spell known by Scion Corporation wizards, which is only as unpleasant as being punched in the back of the head kind of hard.
It should also be noted that no variation of Block Teleport has been found to work on Transport. That is to say, it is currently impossible to block a portal using magic.