The intruders numbered between 10-15 and according to some reports, there are American members of Al Shabab. Two such members are reportedly from Minnesota which has a large immigrant Somalian community... Al Shabab is based in Somalia.
At this point it is unclear the purpose behind the attack, but the Somalian based group claims Kenya's relative prosperity is due in part through the exploitation of the Somalian people. The mall in Nairobi is seen as a sign of that prosperity, and thus became the focus of the attack.
Kenya's military quickly responded with help from the Israeli, French, English, and American governments. At this point there are still hostages inside the mall with Al Shabab refusing to surrender... the group confirmed they were responsible for the attack through their Twitter account.