The conflict of The Metamorphosis centers on the stunning transformation that occurs in its opening line: Gregor Samsa awakens to discover than he is a "monstrous vermin." What follows is Gregor's struggle to accept his new circumstances and to deal with his family's disgust for his body and habits. Even though Gregor becomes more comfortable with himself, he is physically damaged when his father lodges an apple in his back.
This conflict between self and family is only truly resolved when Gregor decides that he must save his family from himself and consciously dies. His family manages to successfully move on with their lives and are freed by no longer having to care for him.
As for the meaning of the story, that is up for debate. At the bare minimum, we can assert that The Metamorphosis explores themes of deep alienation and the consequences that alienation may have in our lives.
The conflict of this story is Gregor's conflict with himself. He is not able to assert his own power in his life. He sacrificing for his family, but to a point that is unhealthy for himself - the extent of his sacrifice is unhappy. He works hard at a job he doesn't like, while none of the other family members work. He has no social life and little happiness. But what is proven through Gregor's transformation is that the rest of the family is perfectly capable of work. As a matter of fact, they thrive despite Gregor's infirmity.
The climax of this conflict is when Gregor makes a move to defend the possessions in his room. His sister, now possessing the power in the family, has chosen to remove them. Gregor gets possessive, however, and defends his furniture. It is the first time that Gregor puts his own interests first. However, the climax is not a permanent shift in power. Gregor quickly reverts to his subservient role, and eventually he willingly accepts death for the family because that is what they want. Even betrayed, Gregor sacrifices.
The resolution of the story is Gregor's death and the future promise for the rest of the family. With the overly self-sacrificing son gone, the family has improved their own prospects and look with hope to the future.