DNA has made a copy of itself during the S phase of the cell cycle as explained by the previous answer. During prophase the DNA condenses into chromosomes. The sister chromatids are being held together by the centromere. The chromatids are exact copies. When the cell continues through mitosis the chromatids separate and each goes to an opposite side of the cell. When all the chromatids are separated the nuclear envelope reforms and cytokinesis occurs. You now have 2 identical copies of each strand of DNA in each new cell. It is in this way that DNA is transferred during cell division.
The Central Dogma of genetics--that is, how the information needed to construct all the proteins for cells--is that DNA is transcribed into RNA, which is translated to proteins. If those words sound like words used in reading a foreign language, it is because that is kind of what is happening. DNA is made up of four types of nitrogenous bases: adenine, guanine, thymine, and cytosine. They are strung in a chain, that makes up DNA. After the DNA is "unzipped" so that it is a single strand instead of a double strand, the DNA is copied by a strand of RNA; only one type of base will attach to the corresponding DNA base. Cytosine attaches to guanine, and adenine, instead of attaching to thymine like it would in a complimentary DNA strand, is instead attached to uracil in RNA. The RNA bases are then "read" in sets of three; each set of three codes for a specific amino acid. The amino acid sequence that results is the specific type of protein coded for by the original strand of DNA.