Following replication, the DNA condenses into chromosomes. At this point, each chromosome actually consists of a set of duplicate chromatids that are held together by the centromere. The centromere is the point of attachment of the kinetochore, a protein structure that is connected to the spindle fibres (part of a structure that pulls the chromatids to opposite ends of the cell).
During the middle stage in cell division, the centromere duplicates, and the chromatid pair separates; each chromatid becomes a separate chromosome at this point. The cell divides, and both of the daughter cells have a complete (diploid) set of chromosomes. The chromosomes uncoil in the new cells, again forming the diffuse network of chromatin.