The historical context of Karbala itself shouldn't be left out of this. Husayn was preparing to lead a rebellion against Yazid I, or Yazid b. Mu'awiya, the second Umayyad caliph who is portrayed as a dissolute tyrant. In the Islamic historiographical tradition, his accession marks the most decisive break between the practices of the rightly guided caliphs and the Umayyad period because whereas previous caliphs had been chosen by acclamation or by a consultative council known as a shura, Mu'awiya had people take an oath to Yazid as heir during his lifetime, thus introducing the dynastic principle into the Islamic community.
Anyway, Husayn was martyred at Karbala. His sister Zaynab was travelling with him, but survived off to the side. This is important for two reasons. One, which you can read about in the account of Abu Mikhnaf (whom for dissertation purposes I'm about to start reading up on), is that she saved Husayn's heir Ali from the massacre, thus ensuring the continuation of the line of Shi'ite imams. More directly relevant to Kefaya symbolism, however, are probably the way she was treated by the regime - being forced to wear fewer clothes than were proper given Islamic modesty - and the fact she bore witness to the tragedy and eloquently told the world of it so all would know of Yazid's tyranny.
There's more symbolism local to Cairo, which thanks to the Shi'ite Fatimid dynasty is one of the claimants to be the final resting place of both Zaynab and Husayn. Zaynab is considered a significant wali in the city, and an important moulid is celebrated in her honor every year. I believe the broom stuff Josh mentioned is connected to that, and I saw a sign that read, "Madad, ya sitt" or "Help, O Lady!" which was clearly invoking her here. Others, however, are better qualified to discuss her importance to Cairo.
One last point - Zaynab was an important figure to the Muslim community even more Karbala, and gained fame as a teacher and scholar in both Medina and Kufa. As such, she has become a key element of Muslim feminists' campaign to do what they see as reclaiming the undeniably important status of women in early Islam. I'm not sure, however, how much that plays into contemporary Egyptian politics.
UPDATE: An account of the protest and its environment is now here.