This post contains spoilers, if you do not know what i am talking about, leave now. This is your only warning.
Part of why i love this show is the depth of story.
When Finn gets the grass sword, he discovers that it is cursed, that he can not get rid of it. When he discovers that the curse can not be broken, that he is stuck with the sword forever, he states "I am cool with that", and the sword goes from being a curse, to a powerful tool.
We see later on, in other seasons that the sword saves his life multiple times,. I would argue that the grass sword is not so much a sword, as it is a mentality. The sword represents his drive to be a hero, to change the world for the better. For some people the responsibility of such an undertaking is destructive, and in history and myth we see heroes destroyed by their responsibilities.
When Finn recognizes his responsibility that is pushed on him with the sword, he decides that this is a fate he can live with. he decides that he is ok with being a hero, that he can cope with it, and do well as one. That is what the meaning of the dreams he has, where the sword is consuming him. It is not so much the sword, but his fate as a hero.