The straight lines of the cross are in stark contrast to the curvature of the crescent, and at first sight, the crescent and the cross seem to represent two very different faiths.
The crescent represents the moon, and by extension, night. The cross represents the Crucifixion of Jesus Christ, and by extension, brilliant light, as with the sun.
And yet these two symbols fit together very well in several different ways.
This combination is used predominantly by the Roman Catholic Church. See Crescent and Cross.
Here's another symbol used by the Catholic Church: Marian Cross.
This double crescent forms a cross. See Double Crescent Cross.
Here we see the Muslim Crescent superimposed on the Christian Cross. See Muslim Crescent and Christian Cross.