A conjunct relates what is said in a sentence to another sentence. As such, it is not part of the structure of the sentence in which it is used.
EG: However, things turned out much worse than expected. ('However' relates what is said to contrast it with previous information about the speaker's expectations.)
All told, we did very well. ('All told' connects information that has already been given to produce a final conclusion that connects everything. In both examples it is possible to remove the conjunct without making the sentence ungrammatical.)