Hacktivism is a 'hack', propagated by hackers, that is motivated by a political or social cause. Hacktivism is typically conducted on the Internet, and usually involves accessing or disrupting computer systems that are connected to the Internet. The term 'hacktivism' is a combination of the terms: hack and activism.
Hack: process of exploiting a vulnerability in a computer
Activism: an effort to promote a political, social, environmental cause or change.
Denial-of-service attacks are a popular 'hack' used by hacktivists; a DoS attack attempts to make a computer system unavailable to users of that system. The Anonymous (group) is renowned for conducting distributed denial-of-service (DDoS) attacks on a range of websites owned by companies/governments they have targeted for a hack.
In 2014, the most famous hack blamed on hacktivists was conducted against Sony Pictures. Sony Pictures decided to cancel the release of The Interview; a movie, and comedy, that was related to North Korea. Sony Pictures were the victims of one of the most serious cyber attacks ever inflicted upon an American business; it is claimed that terabytes of sensitive data was stolen from Sony. The group claiming to have conducted the hack is named: the Guardians of Peace. They also threatened terrorist acts against cinemas that showed the film.