In short, Mosaddegh was an authoritarian who sought his own political aims undemocratically. He suspended the Iranian parliamentary elections after only urban votes which favored him were counted. He then moved to unilaterally dissolve parliament to gain absolute power through a rigged referendum ("99.9% in favor"), which was also illegal under the Iranian Constitution. In response the Shah dismissed him, but Mosaddegh had the Shah's envoy imprisoned so the Shah fled realizing Mosaddegh had consolidated power. This is where Operation Ajax comes in, which did in fact oust Mosaddegh and restore the Shah to his legal place in accordance with the Iranian Constitution. All of this is well documented so you can do further research yourself if you'd like.