When you start the PCR amplification reaction, you have a template which has sequences where the primers will anneal. The forward primer anneals in the sense strand and the reverse one in the complementary sequence (see attached figure).
After the first PCR cycle, two types of fragments are obtained. First those which come from tha 5'-3' sequence, that are 3'-5' and will anneal the reverse primer in the following cycle. This fragments have the correct 3' end, but the 5' includes part of the template that doesn't correspond to our target (see attached figure)
Second, those fragments that come from the 3'-5' sequence, that are 5'-3' and will anneal the forward primer. This fragments also have the correct 3' end, but the 5' includes part of the template that doesn't correspond to our target (see attached figure).
Now, during the second cycle, are produced the first fragments that have the precise length of the sequence that we want to amplify (see attached figure).
So, it's not until the third cycle that the reaction starts amplifying exactly the sequence of desired length.