A rectified tile is a tile that has been cut after manufacture to ensure that it is truly square. For example, a production batch of ceramic tiles which have been manufactured at 305mm x 610mm will all be re-cut to 300×600 at the same time to ensure they are all the same size and are truly square.
The reason why tilers charge more to lay a rectified tile is that typically they are laid at 1.5mm spacing (minimum allowed by Australian standards) to provide a beautiful finish. This is more difficult to lay than wider spacing as wider grout lines give more room for movement during installation. If the tiles are rectified and the grout line is 1.5mm then the tiler must ensure that the substrate is as level and perfect as possible. The thinner grout lines also mean that there is less room for error. This is time consuming work and so the installation cost reflects the extra time and care required for the job.