The hospital is the place where every player (it doesn't mind if you are in a faction or not) respawn after death.
If your character, by any chance, dies you will have to wait 15 seconds inside the hospital until your character is rested and re-healthed and then you will respawn on the Hospital's entrance.
Also, if your character is in the EMT / Medics faction you will respawn here everytime you log in.
Where do I find the Hospital?Edit
You will find the Hospital on West of San Fiero, near the west beach.