It's a suffix that is added to a noun to form a noun that denotes a person who is associated with or practices that which the noun refers to.
For example:
* Art + -ist = Artist (a person who practices art)
* Capital + -ist = Capitalist (a person who supports capitalism)
* Social + -ist = Socialist (a person who supports socialism)
While "-ist" itself is not a root word in the traditional sense, it functions as a suffix that forms new words.