All DVD's do have the same resolution (ignoring region/country specific differences like PAL). However, the files on DVD's are compressed. If all other things are equal (and that's a huge IF), less compression = better picture.
Superbit is a trademark of Sony. Their basic idea is to have a line of DVD's that limit the number of extras on the disc so they can use as little compression as possible when fitting the movie on the disc. Keep in mind that this is just a marketing name, not any sort of standard. Some DVD's produced by other studios have equal or less compression than Superbit DVD's, but can't use that marketing name.
A secondary idea behind Superbit DVD's is that it doesn't make sense to give a movie a high bitrate (high bitrate = low compression) if you aren't starting with a good print/transfer to begin with. For the most part, Sony has done a good job and started with good prints/transfer for the Superbits. TFE is perhaps the best example of the process working; good starting point, well produced, high bitrate all add up to one fine looking movie.
Since Superbit DVD's are just standard DVD's, you don't need any special equipment to take advantage of them. However, the better your display device, the more you will notice the difference over DVD's with more compression or worse transfers.
PS -> Anyone else starting to think we need a "sticky" on Superbits?