The mRNA gets translated into the spike protein. And then the cell presents it in the surface for the immune cells to track and learn it. This is called MHC-I pathway. As a consequence of this, the immune system might instruct "infected" cells to self-destruction.

There are also other delivery pathways for mRNA vaccines.

The virus is not functional because the mRNA vaccine only contains one little component of the virus, the spike protein.

You can see a quick comparison chart of the most important vaccine methods in this Nature figure: https://media.springernature.com/lw685/springer-static/image...