Most images on websites are saved as JPEG files, which are very compact and so are quick to download. However, JPEG files do not support transparency, so are not suitable for the cutouts available on this site.
TIFF files can contain multiple layers, and because they use no compression offer high image quality. They tend to be large, however, so can take a long time to download.
This is a new file format based on JPEG, but which supports transparency in single layer images. The quality is much higher than JPEG, as it uses a different compression mode. All single layer images on this site are offered as JPEG2000 files as well as TIFFs, for speed of download.
As of version 7, Photoshop does not load the JPEG2000 plug-in by default. You will find it on the Resources CD that came with your copy of Photoshop, in the folder Goodies / Photoshop / Optional Plug-ins / Photoshop Only / File Format. (NOTE: the precise location may vary with different editions of Photoshop.)
Copy the file JPEG2000.plugin to the Plug-ins folder inside the Photoshop folder on your hard disk, and restart Photoshop. You will now be able to use JPEG2000 files using the standard Open and Save dialogs.
There are many reasons why you may not have the original disks. If this is the case, you can download a compatible plug-in from the fnordware website. Copy the file j2k.plugin to the Plug-ins folder inside the Photoshop folder on your hard disk, and restart Photoshop to use JPEG2000 files using the standard Open and Save dialogs.