In traditional Japanese arts the ranking is usually organized according to two different "ladders": in the first one, which is vaguely equivalent to being in elementary school, the ranks are called kyū (級) and the progression goes from "high" to low… i.e. you start as sixth kyū (but in some schools/styles you may have to start a 10th!) and by passing an exam you get promoted to fifth kyū , then fourth and so on.
Until you get to first kyū. From there you get promoted to ShoDan: 初段 (i.e. - roughly, "first Dan", but as we will see below it's not quite so simple), which takes you to the bottom of a new "advanced" ladder, where ranks increase, so you will later get NiDan (Second Dan) and so on.
This type of progression (and organization) is common to all Japanese disciplines: for sure it is used in martial arts (and in that case ShoDan means you can wear a black belt), and it's the way used to assess Go players ranking, calligraphers' skill and so on.
So now I am a ShoDan in Hanshi style calligraphy (and I am also a SanDan - i.e. 3rd Dan - in Aikido). What does this actually mean?
Let's start with a bit of etymology. The ideogram for Dan is the composition of a radical representing a ladder. (Some even say it more specifically represents "a very steep path on the side of a cliff, one where you have to use crude steps cut in the rock in order to proceed"). This is the left part here, with the red arrow:
The rightmost part (blue) is a radical that is usually connected to the idea of use of weapons, martial endeavors. So basically, the whole gives us "a step in the study of a discipline".
Before going on with analyzing "Sho", let me add that for Dan after the first you just use a "numeral". I.e. for second Dan you use 二 (which means just 2 or "second") … for "fourth" you'd use the numeral for 4 (i.e. 四).
For the first one, though, you don't use the numeral for "one".
You use this:
Leftmost element means "Clothes, dress", the right one (in blue) is "blade, knife". The whole represents the idea of "in order to make clothes you start by cutting cloth first".
The whole ideogram means "Beginner. The lowest possible rank". I.e. in a modern army, this would probably be the equivalent of someone just out of Basic Training.
Got it? "ShoDan" is not "I am the equivalent of a Green Beret in whatever discipline I am currently studying". In fact, it means you just passed your driving license test, and that in due time you may even be able to park your car in less than 23 maneuvers.
This is something that martial art masters always try to remind their students of: obtaining your black belt should never be an end in itself - because you have just proved the most elementary grasp of the superficial technical aspects of what you are doing.
(Specifically my own Aikido teacher always repeats to everyone: "Receiving a Rank in Aikido only proves that you were a passable specimen of the previous rank abilities - i.e. getting your 2nd Dan means you have demonstrated that you are a decent ShoDan, nothing more").