As Arnisador said, it depends upon the art. In order to get a better idea of the dan ranking system, it is necessary to have some information about where it came from. Jigoro Kano, the creator of modern judo, was the first to apply the dan, or step, ranking system to the martial arts. He was a school teacher and saw that the swim teams used this system. He thought it would be a good way of differentiating skill levels in his newly created judo. It proved very popular, and was adopted by the Japanese karate systems when they began to become prominent in Japan in the early 1900's.
Today, the majority of schools use a dan ranking system, usually consisting of ten steps. Ten is an arbitrary number though, and I know of at least one organization that is up to fifteen dan ranks. Many of the old koryu arts use both dan ranks and menkyo certificates, or don't have any dan ranking at all. The problem in any ranking system is that it is only applicable
within a given system. There are many umbrella organizations which grant dan ranks. These are meant to maintain consistency across schools, usually for competition as in judo or kendo. Due to the veritable plethora of umbrella organizations within the karate community, it is very difficult to assign a skill level based solely upon dan ranking within a particular art. Since there is no oversight organization for the martial arts (thank goodness!), it is up to individual organizations to set criteria as to what constitutes a proper skill level for any particular rank.
Most people who aren't directly involved in the martial arts, and many who are, don't understand that any rank is irrelevant outside of the organization that granted it. Many older organizations that have well publicized (not to mention difficult) criteria for their rankings are acknowledged amongst themselves. A hachidan (8th dan) in kyudo with the all Japan kyudo federation would be granted the honor due to a hachidan within the all Japan kendo federation, as would a hachidan within the all Japan iaido federation. Organizations such as these are well known and familiar with each other. Meanwhile, if you take a hachidan from the American jujitsu Federation (just to pull a name out of my hat), they'd have no idea what to make of him although, being Japanese, they'd still be polite.
Therefore, it is pretty hard to answer your question without knowing the specific art to which you refer.
Hope that helps, and doesn't just confuse things!