Why 3' and 5'? The carbon atoms of the deoxyribose sugars are numbered. The sugars and phosphates ("legs" of the ladder) are strongly bound by 3'-5' phosphodiester bonds; the phosphodiester bonds link the carbon atoms number 3 and number 5 of the successive sugar subunits. The 5' end of the DNA molecule will have a sugar subunit in which the carbon atom number 5 is not linked via a phosphate to a neighboring sugar subunit. It is labeled as the 5' end of the molecule. Likewise, the 3' end of the DNA molecule will have a sugar subunit in which the carbon atom number 3 is not linked via a phosphate to a neighboring sugar subunit. It is labeled as the 3' end of the molecule. Notice in the diagram that the 5' end of the molecule terminates in a phosphate while the 3' end terminates in a hydroxyl(-OH). For this reason, the DNA molecule is described as antiparallel because one strand runs such that the 5' to 3' is opposite to that of the other strand. The sequence of bases in DNA is usually written with only one strand in the 5' to 3' direction; the other strand sequence can be inferred from this original. Using the diagram to your right, TGCATG describes the molecule while ACGTAC is inferred by that sequence of bases. These two strands of the double helix are described as complementary.

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