Primer3 is a widely used program for designing PCR primers (PCR = "Polymerase Chain Reaction"). PCR is an essential and ubiquitous tool in genetics and molecular biology. Primer3 can also design hybridization probes and sequencing primers.
PCR is used for many different goals. Consequently, primer3 has many different input parameters that you control and that tell primer3 exactly what characteristics make good primers for your goals.
Primer3 -- the C code, the web interface, and the documentation -- are an open source, community-development project hosted by GitHub.