Lit. step in
Japanese, the dan grades are used to denote
rank in the Japanese
martial arts (
budo).
The equivalence with "black belts" is a modern (20th century?) invention, brought about by karate-do's use of colored belts to denote rank. In kendo, iaido, kyudo, and naginata-do, insignia of rank are not used, except perhaps for small children at the kyu levels.
At least in kendo, advancement through the dan ranks becomes progressively more difficult as one goes up (it's not linear). In fact, this is enforced through minimum wait times between passing a dan test and being allowed to test for the next one, and increasingly more stringent standards. In kendo, this is one year per dan level, i.e. if one passes a yondan (4-dan) test, one must wait four years before testing for godan (5-dan).
As an example, at the last shinsa (testing) I attended, all eight shodan (1-dan) candidates passed (including me), but of the eight nidan (2-dan) candidates, only three passed.