The Egyptian unrest has provided a real test case in how social media and web culture can be used in political hotspots. Now, Anonymous, the amorphous and unidentified group of hackers who provided so much drama during the Wikileaks furor late last year, are evidently going after Egyptian governmental web sites.
Sites belonging to Egypt's cabinet, the Ministry of the Interior and the Ministry of Communications and Information Technology were inaccessible, most likely due to distributed denial-of-service (DDoS) attacks, as of 3 p.m. EST.
Members of Anonymous had begun to organize at attack on Egypt three days ago, according to the Web-hosting company Netcraft, but the effort picked up steam Tuesday as the authorities in Cairo blocked domestic Twitter access.
That last bit answers your question of why Anonymous would care about Egyptian politics. It's not so much about the policies of Mubarak, it's that they blocked Twitter and Anonymous is(/are?) rabid advocates of free and open internet.