The meaning of the word Souk is for an an open-air market place and tradiotonally originates from Western Asia and North Africa. More often you will actually see the word used with a "Q" and as Souq, which is more often associated with Arab traditional markets.
There are many Souks in Dubai such as the Gold Souq and the Spice Souk in Deira and near to the Dubai Creek. There is also the Textile Souk which is based in Bur Dubai the other side of the Creek.
For the more modern Souk, head to either Madinat Souk or Souk al Bahar. Links to these below: