In all cells, DNA sequences are maintained and replicated with high accuracy. The
mutation rate, approximately 1 nucleotide change per 10⁹ nucleotides each time the
DNA is replicated, is roughly the same for organisms as different as bacteria and
humans. Because of this remarkable accuracy, the sequence of the human genome
(approximately 3 x 10⁹ nucleotide pairs) is changed by only about 3 nucleotides each
time a cell divides. This helps in passing the accurate information to the subsequent generation

How DNA replication occurs with such accuracy?

DNA templates help in binding to the complementary DNA sequence. This process entails the recognition of each nucleotide in the DNA template standby a free (unpolymerized) complementary nucleotide, and it requires the separation of the two strands of the DNA helix. DNA polymerase enzyme is used for the following process

During DNA replication in the cell, both the DNA strands serve as DNA templates to form new strands of DNA. Because each of the two daughters of a dividing cell inherits a new DNA double helix containing one original and one new strand, the DNA double helix is said to be replicated “semi conservatively” by DNA polymerase

Chapter 5: DNA Replication, Repair, and Recombination - Biology ...
The DNA double helix acts as its own template

The DNA replication is the  continuous growth of both new strands, at the replication
fork as it moves from one end of a DNA molecule to the other. But because of the antiparallel orientation of the two DNA strands in the DNA double helix, this mechanism would require one daughter strand to polymerize in the 5′-to-3′ direction and the other in the 3′-to-5′ direction. Such a replication the fork would require two distinct types of DNA polymerase en4/mes. However, all of the many DNA polymerases at have been discovered can synthesize only in the 5′-to-3′ direction. How then, can a DNA strand grow in the 3′-to-5′ direction? Researchers added highly radioactive U-thymidine to dividing bacteria for a few seconds so that only the most recently replicated DNA-that just behind the replication fork-became radiolabeled. The transient existence of pieces of DNA that were 1000-2000 nucleotides long, known as Okazaki fragments. It is polymerized in 5′ – 3′ direction

The High Fidelity of DNA replication requires several Proofreading Mechanisms. DNA polymerase performs the first proofreading step just before a new nucleotide is added to the growing chain. The correct nucleotide has a higher affinity for the moving polymerase than does the incorrect nucleotide because the correct pairing is more energetically favourable. The enzyme must undergo a conformational change before the nucleotide is covalently added to the growing chain. The change occurs more accurately to the correct base pairing, which let polymerease to “double-check” the exact base-pair geometry before it catalyzes the addition of the nucleotide.
The next proofreading reaction, exonucleolytic proofreading takes place immediately after incorrect nucleotide is added to the growing chain. DNA polymerase enzymes are highly discriminating in the types of DNA chains they will elongate: they absolutely require a previously formed base-paired 3′-oH end of a primer strand. Those DNA molecules with a mismatched (improperly base-paired) nucleotide at the 3′-oH end of the primer strand are not effective as templates because the polymerase cannot extend such a strand. DNA polymerase molecules correct such a mismatched primer strand by means of a separate catalytic site. This 3-to-5 proofreading exonuclease clips off any unpaired residues at the primer terminus, continuing until enough nucleotides have been removed to regenerate a correctly base-paired 3′-oH terminus that can prime DNA synthesis.

In this way, DNA polymerase functions as a “self-correcting” enzyme that removes its own polymerization errors as it moves along the DNA. The self-correcting properties of the DNA polymerase depend on its requirement for a perfectly base-paired primer terminus which is not possible by the enzyme.

The RNA polymerase enzymes involved in gene transcription do not need such an efficient exonucleolytic proofreading mechanism i.e errors in making RNA are not passed on to the next generation, and the defective RNA molecule has no long-term significance. RNA polymerases are thus able to start new polynucleotide chains without a primer. There is an error frequency of about 1 mistake for every 10⁴ polymerization events both in RNA synthesis and in the separate process of translating mRNA sequences into protein sequences. This error rate is 100,000 times greater than that in DNA replication, where a series of proofreading processes makes the process unusually accurate

Now you know the need for DNA replication only in the 5′-to-3′ direction. If there were a DNA polymerase that added deoxyribonucleoside triphosphates in the 3′-to-5’direction, the growing 5′-chain end, rather than the incoming mononucleotide, would provide the activating triphosphate needed for the covalent linkage. In this case, the mistakes in polymerization could not be simply hydrolyzed away, rather the DNA synthesis would be terminated

It is, therefore, possible to correct a mismatched base only if it has been added to the 3′ end of a DNA chains.

So Many DNA Polymerases, So Little Time | GoldBio
Exonucleotide proofreading by DNA polymerase during DNA replication