What is the basis for the difference in how the leading and lagging strands of dna molecules are synthesized?

The answer is because DNA polymerase adds new nucleotides only to the 3' end of the template strand.

DNA molecule consists of two strands. One of the strands (3'-5' direction toward the fork) is called leading and it is replicated continuously. The other strand is called lagging strand  (5'-3' direction toward the fork) and it is replicated discontinuously. After DNA helicase opens the replication fork, these two strands are free and they wait for complementary nucleotides. However, DNA polymerase adds new nucleotides only to the 3' end of the template strand. Since the leading strand' free end is 3' end, DNA polymerase easily adds nucleotides at the 3' end toward the 5' end (direction 3' to 5'). The free end of the lagging strand is 5' so DNA polymerase cannot start from that end. Therefore, the replication starts on the several places of the lagging strand so DNA  polymerase can add nucleotides at the 3' end toward the 5' end.