The trikirion symbolizes the Holy Trinity and the dikirion the dual nature of Christ: God and man.
(H/T Rorate Caeli)
On a related note: this evening I will be attending the annual meeting of the Fellowship of St. Alban and St. Sergius in Copenhagen. The fellowship exists to promote unity between Eastern and Western Christians - mostly Orthodox and Anglicans/other traditional Protestants, respectively, but I'll try to have some Catholic viewpoint thrown in. In fact, the unity which the fellowship seeks is already effected in the Catholic Church, where Eastern and Western Christians are even now under the same roof, united in doctrine and with equal rights and dignity - but unfortunately most of those involved in the fellowship don't realize that that unity is already there and just waiting for them to join in.