It is how DNA works in the case of PCR, for example. The denaturation cycle splits double stranded DNA into individual single strands, which can be thousands of base pairs long. Primers are short sequences that bind to these single strands. If there are only one or two mismatches, the primer can easily bind to the wrong part of the DNA strand, if the temperature during the annealing step is low enough. This causes messy gels and incorrect DNA products in the PCR.

In some cases, if the temperature is very low, the primer can bind to sequences with many mismatches. This results in the scientist crying and finding god.