selectable marker
When you transform bacteria with a plasmid, most of the cells fail to take it up — only a small fraction succeed. You need a way to find the needles in the haystack: a test that kills the failures and lets the successes survive. A selectable marker is a gene on the vector that gives its host a survival advantage under a chosen condition, so only cells carrying the vector live.
The most common selectable marker is an antibiotic-resistance gene — for instance, a gene whose protein breaks down or pumps out the antibiotic ampicillin. You spread your transformed bacteria on an agar plate laced with ampicillin. Cells that took up the plasmid carry the resistance gene, make the protective protein, and grow into colonies. Cells that did not take up the plasmid have no protection and die. The plate has done your sorting for you: every colony you see must contain the vector. Other markers work by supplying a nutrient the host cannot make on its own, so only vector-bearing cells grow on minimal medium.
Selection is the step that makes cloning practical — without it you would be hunting through a billion identical-looking colonies for the rare one that worked. Note the important distinction: a selectable marker tells you the cell took up the vector, but not whether your insert is actually in the vector. That second question — empty vector versus recombinant vector — is answered by a separate screening step such as blue-white screening.
Transform E. coli with an ampicillin-resistance plasmid and spread them on ampicillin plates. Tomorrow you see, say, 200 colonies on a plate that started with millions of cells. Those 200 are exactly the cells that took up the plasmid; the millions that didn't were killed by the antibiotic overnight.
Antibiotic in the plate kills everything that lacks the resistance marker.
Selection confirms uptake of the vector, not insertion of your gene — an empty re-circularized vector still survives the antibiotic, which is exactly why a second screen for recombinants is needed.