“I was polishing a brandy snifter when the Unmarried Mother came in. I noted the time—10.17 p.m. zone five or eastern time November 7th, 1970. Temporal agents always notice time & date; we must.” 

The bartender is a time traveler who works for the Temporal Bureau. The Unmarried Mother is someone the bartender must recruit to become a time agent.

“The Unmarried Mother was a man twenty-five years old, no taller than I am, immature features and a touchy temper. I didn’t like his looks—I never had—but he was a lad I was here to recruit, he was my boy.” 

The narrator/time traveler works as a bartender at Pop’s Place. He’s been expecting the Unmarried Mother—a young man who makes his living writing an advice column as if he were a woman—whom the narrator must manipulate so that the timeline will work out properly.

“His fingers tightened on the glass as he seemed about to throw it at me; I felt for the sap under the bar. In temporal manipulation you try to figure everything, but there are so many factors that you never take needless risks.” 

The bartender’s time-travel job requires him to insert himself into the stream of events at just the exact moment, and behave precisely, to create the correct effect on the timeline. This is very hard to do, and problems happen, which is why time travel can be so dangerous.