Prophase is a stage of mitosis. In prophase the genetic material (DNA), which normally exists in the form of chromatin, condenses into a highly ordered structure called a chromosome. Since the genetic material has been duplicated, there are two identical copies of each chromosome in the cell. Identical chromosomes (called sister chromosomes) are attached to each other at a DNA element present on every chromosome called the centromere.
When chromosomes are paired up and attached, each individual chromosome in the pair is called a chromatid, while the whole unit (confusingly) is called a chromosome. Somewhat confusingly, when the chromatids separate, they are no longer called chromatids, but are called chromosomes again. The task of mitosis is to assure that one copy of each sister chromatid - and only one copy - goes to each daughter cell after cell division.
The other important piece of hardware in mitosis is the centriole, which serves as a sort of anchor. During prophase, the two centrioles - which replicate independently of mitosis - begin recruiting microtubules (which may be thought of as cellular ropes or poles) and forming a mitotic spindle between them. By increasing the length of the spindle (growing the microtubules), the centrioles push apart to opposite ends of the cell nucleus.