Warning: Episode 5 spoilers ahead! In the world of The Handmaid's Tale, someone is always watching. The Republic of Gilead was set up to guarantee it: citizens are pressured to spy on one another and report on anyone who misbehaves, or else suffer dire consequences. But the surveillance in Gilead isn't wholly self-sustaining; there is also a secret police force called the Eyes of God. There's no way to know for sure if someone is an Eye. In the very first episode of the series, Ofglen warned Offred that there was an Eye living in her house, so she had to be careful. The only possibility was Nick; women couldn't be Eyes and he was the only man in the house besides the Commander. But is Nick really an Eye on The Handmaid's Tale?
If viewers take Nick at his word, then yes, he is an Eye. Offred had her suspicions from the start, but in "Faithful" she finally asked Nick point-blank if he was an Eye. Though he evaded answering the first few times, he did eventually confirm that he was, even semi-sarcastically telling her to go up to bed or he'd report on her. But there might be more to it than that. Nick could be an Eye, but that wouldn't necessarily mean he was a true believer in the Republic of Gilead. Nick had plenty of opportunities to report on Offred, but he never did. Instead he warned her of danger and encouraged her to stay safe, which could mean he's one of the good guys.
If Nick isn't a genuine follower of Gilead, then there are two possibilities that would explain why he's an Eye. He could have been conscripted into the Eyes, in which case he wouldn't have a choice. It's possible that he's just trying to survive and keep his head down, but not cause trouble for anyone. That would be in line with certain things he's said to Offred about not being able to change their circumstances. "You can't change anything about this," he told her in Episode 3. "It's going to end the same no matter what you do, so there's no use in being brave. Brave isn't a part of this... Everybody breaks. Everybody."
However, there is another possibility. Nick might be using his position as an Eye to gather information for Mayday, the underground resistance in Gilead. It would explain why Nick is so concerned with keeping up appearances (always warning Offred, and even agreeing to Serena Joy's secret insemination plan in Episode 5), but never follows through with actually tattling on Offred. If Nick is an Eye who genuinely believes in the cause, then he's not doing a great job of it. He said he was an Eye, but he doesn't act like one.
Whether or not Nick is a member of Mayday is uncertain, but he definitely doesn't seem like a dedicated soldier for the Eyes of God.