There are several forms of Catholicism but essentially all are in 'communion with' the Papal authority in Rome. There are approximately 1.1bn Catholics around the world, and they share the doctrines, beliefs and creed which is claimed to have been passed down directly from the founder - Jesus of Nazareth - via St Peter. The institutions of the Catholic Church claim that they are the successors, arbiters and interpreters of his teachings and have had a profound effect on European history and culture for nearly 2000 years. The church grew in Rome in the Empire period and gained political power as the Roman state declined.
Catholics all around the world look to the Pope as their spiritual leader. The Pope is elected from cardinals (similar to a board electing a chairman) and he serves for life. Because only men can be in the clergy, only men can attain positions of leadership. Women do have some roles but they tend to be servile and very local positions.
In recent years the Catholic church has faced many scandals around the institutionalised treatment of women, children, and vulnerable people. Large numbers of clergy have been running paedophile rings along with near prison/slave conditions in orphanages and schools, all being presided over and covered up for years by the hierarchy. Despite condemnation from governments around the world, the church offers some mea culpa then goes straight back to ignoring the abuse (and quietly moving on the perpetrators) until another scandal comes out.