Screening recombinants.
Only a cell that took up a plasmid which has the amp^R gene will reproduce and form a colony.
Cells with non-recombinant plasmids have a functional lacZ enzyme that allows them to digest sugar and form blue colonies.
Some of the recombinant clones have a disrupted lacZ gene; they will form white colonies.
These white colonies can be analyzed to identify those carrying the gene of interest.