Nick is the father of June's unborn child, who's conceived per Serena Joy's request for them to sleep together. Nick and June later develop feelings for each other. When guards take June away, he tells her to just "go with them." If Nick doesn't end up betraying June, it's likely that their relationship will intensify over the course of the second season.
We learn a little bit about Nick's backstory in the later part of the first season. He's a part of Gilead's secret police, the Eyes, in addition to working for Fred Waterford's family. Before Gilead, Nick was just a normal guy looking for a job, a mundane reveal that belies his strong, silent-type persona. While job hunting, he lands a job with the Sons of Jacob, a group that had a hand in starting Gilead.