What does "station" mean in "separate and equal station" in the Declaration of Independence?

The short answer to this is that the word "station" means
something like "status." What this part as a whole means is that if you have a status
that is separate (from other countries) and equal (to other countries) you are an
independent nation.

You can see this meaning from what the
rest of the sentence says.  Basically, what this sentence says is that countries have to
give reasons if they are going to break the ties that have connected them to some other
country (like the ones that connected the colonies to England) and become their own
separate and independent country (this is where the line you cite comes
in).