The sun and the moon do not actually contact each other since they are millions of miles apart. However, from the reference point of the earth, there are times when it appears that the edge of the moon's disk begins to overlap with the edge of the sun's disk.
First contact is when the moon just begins to pass in front of the sun.
Fourth contact is when the moon stops blocking the sun. This happens when you view a total or annular eclipse. This is best illustrated using an annular eclipse, when the moon appears to have a smaller size than the sun. First and Fourth contacts are said to be external contacts, where there is no overlap. The second and third contacts are when the edges of the disks contact each other, but one disk is inside the other.