"ŝanĝi" is to change <someone or something> (i.e. to alter <someone or something> or even to replace <someone or something>. It's a transitive verb, which means that it always requires a direct object.
"ŝanĝiĝi" is to change, i.e. to undergo a change or to change itself/oneself. It's an intransitive verb, which means that it cannot take a direct object.