The basic meaning of the old word hence is "from here" referring to movement from one place to another.
In analogy it can express the cause of something. "From here (place)" extends its meaning to "from this cause given here in the sentence before".
Now it means "therefore".
In The Free Dictionary, hence, you see that dictionaries give the meaning often in an wrong order of arrangement so that you don't get an understanding of a word. The primary meaning is "from here". All other uses are simple semantic developments of the basic meaning. The Free Dictionary has the meanings arranged according to frequency of uses and the primary meaning is number 3a. So it is no wonder that you don't look through as to "hence".
There are three such old words: hence, thence, whence
hence means from here
thence from there
whence from where
The formation can best be made understood with English, German and Latin
hence - here von ex (here from out).
This is no historical explanation. It only wants to give an idea of how these words are formed.