Niles (David Hyde Pearce) was in love with Daphne (Jane Leeves) the moment he met her, but despite how obvious it was, she never realized it until it was explicitly pointed out to her in later Cheers spin-off was launched to continue capitalizing on the Boston-set sitcom after it ended. Frasier's focus was on fan-favorite Frasier Crane (Kelsey Grammer), who moved back to Seattle to become a radio psychologist. But despite having a titular character, the show was very much an ensemble series.
Frasier's homecoming meant the introduction of his family — Martin Crane (John Mahoney), the family patriarch, and Niles, his younger brother, who was also snootier and snobbier. Daphne was brought in to be Marty's home health care provider, helping him recover from an injury. But over time, she had become almost a member of the family since she also lived in Frasier's swanky Seattle apartment. While Niles was married to Maris, he was immediately infatuated with Daphne. Even though both of them dated different people over the next several years, he had only become more in love with her. Frasier even used his attraction for laughs as he couldn't contain himself around her most of the time.
Given how obvious it was, it's curious why Daphne never realized that Niles was secretly harboring a crush on her until a drugged Frasier blabbed about it. Eventually, Roz Doyle (Peri Gilpin) confirmed it, but even then, she was surprised that he would be attracted to her. There is a couple of reasoning for this, but the Frasier episode titled "Perspectives On Christmas" properly summed it up. In it, a series of events was told from different points of view. When it was Daphne's turn, she saw her interactions with Niles differently than how everybody did. She didn't even notice the little things Niles did to get closer to her, which included giving her multiple hugs in an effort to supposedly console her instead of him just wanting to have any kind of physical interaction with her. No wonder, until someone clearly pointed it out, she was mostly oblivious to Niles' feelings.
So, why was Daphne blind to Niles' antics in the first place? This may boil down to her own perception of the Crane brothers, especially Niles. When Frasier was first introduced in Cheers, he stood out because of his snobbiness amidst the eponymous bar's usual clientele. When the character transitioned into his own series, the spin-off creators had to tone him down slightly. For both comedic and narrative purposes, they introduced Niles, who was much more elitist than he ever was. Because of this, Daphne may have never thought that Niles would be interested in her. So, although he was fawning over her every single time they would see each other, which was fairly frequent since Niles would always visit his brother and dad, she remained unaware of his feelings.
Frasier is one of the few spin-offs that became as successful as its parent series. Whether or not it's better than Cheers remains a big topic of conversation among sitcom connoisseurs, but one thing is sure. The offshoot elevated the will-they/won't they trope popularized by Diane (Shelley Long) and Sam (Ted Danson) via Niles and Daphne's story.