Direction
The ribose sugar in the sugar-phosphate backbone of DNA contains five carbons, so biologists refer to the two directions along a DNA strand as 5' and 3'. The 5' end of the DNA strand has a phosphate group, while the 3' end has a hydroxyl group. DNA replication always goes in the 5' to 3' direction. If you draw the strand on a piece of paper with the 5' end at the top, regardless of where you start, replication along that strand would travel toward the bottom.
Antiparallel
The two strands in a DNA molecule are antiparallel; if you travel 5' to 3' along one strand, you are traveling 3' to 5' along the other. The 5' to 3' direction along one strand is the opposite of the 5' to 3' direction in the other. This feature makes replication somewhat more complicated, because replication occurs at sites called replication forks. Since DNA replication can only proceed in the 5' to 3' direction, at each replication fork, replication must proceed toward the fork along one strand and away from it along the other.
Replication Forks
Replication begins at sites called origins of replication where the DNA strands unwind, creating a "replication bubble." The two points at either end of the bubble are called replication forks and these spread outward as replication progresses. At each replication fork, replication or copying of the DNA along one strand is continuous, because that strand is exposed in the 5' to 3' direction. This strand is called the leading strand. The other strand must be replicated in a direction running away from the replication fork and this strand is called the lagging strand.
Okazaki Fragments
The lagging strand is replicated in short discontinuous fragments called Okazaki fragments. Each is synthesized beginning with a short piece of RNA whose formation is catalyzed by an enzyme called RNA primase. A DNA polymerase enzyme later replaces the RNA primer with DNA and an enzyme called ligase joins the fragments together. Synthesis along the leading strand, by contrast, is much simpler; the DNA polymerase can follow behind the replication fork and add more nucleotides to make a continuous strand.