This one was a toughie. But it turns out that at each growing fork there is continous synthesis of one new strand—the 5’ to 3’ strand or leading strand--and discontinous synthesis of the 3’ to 5’, or lagging strand. As polymerase proceeds along the growing fork, it takes time to sort of back up and synthesize little discontinuous chunks of the lagging strand, after laying down a primer for each one. What a pain! These discontinous Okazaki fragments (after Reizi Okazaki, the biologist who discovered them) are thus separated by RNA primers, which must then be dissolved and filled in with DNA nucleotides, then sealed shut by ligase. 

Figure 14. Replication of DNA by DNA polymerase. The polymerase activity is denoted by P, shown synthesizing the continuous leading strand (left), and the discontinuous lagging strand (right).  Polymerase synthesizes the leading strand toward the top of the figure and lagging strand toward the bottom of the figure---both in the 5' to 3' direction. The lagging strand is formed in fragments initiated from RNA primers  (in red) laid down by primase. The fragments are then sealed by ligase. Helicase (H), unwinds the DNA to expose parent strands for replication.