As a series, Community's focus was squarely on Jeff Winger's study group. And while the members frequently fluctuated, particularly once actors started moving on, one thing that didn't change was all the romantic relationships between them. One of the series' biggest relationships involved Jeff and Annie. It was filled with flirting and endless "will they, won't they" moments. Fortunately, they never did, which was ultimately the right move for the show.
When Jeff decided to form the Spanish study group in Season 1, Episode 1, it was purely to sleep with Britta Perry. At the time, Jeff hadn't figured out that she was the worst and was still interested in her. While they were never officially a couple, Jeff and Britta spent a surprising amount of time hooking up behind the scenes in Community's first couple of seasons. Eventually, that all fell apart, and they both moved on with their lives.
At the same time as Jeff's booty call relationship with Britta was happening, Annie's infatuation with Troy Barnes was still going strong. They had gone to high school together. However, unfortunately for Troy, she had already started a relationship with Britta's ex-boyfriend by the time he realized that he wanted to ask her out -- but that wasn't the real problem.
Hiding behind this web of dysfunction, Annie harbored a crush on Jeff that kept growing until it finally manifested in Season 1, Episode 25. Professor Slater and Britta publically tried to make Jeff choose between them at one of Greendale's many dances. In response, Jeff bolted. He then ran into Annie out front of the building and ended up kissing her quite passionately. This complicated the situation incredibly when Season 2 started.
Throughout the rest of the series, Community danced around the mutual infatuation between Jeff and Annie without doing anything about it. When the show came to an end in Season 6, Episode 13, Annie and Abed finally left Greendale behind to pursue new careers. Jeff stayed, continuing to work at Greendale alongside Ben Chang, Dean Pelton and Frankie Dart. Britta was also around, working as a bartender, which was the first stable job she had.
Jeff briefly considered asking Annie to stay at one point but changed his mind when he realized it was better for her to leave. It was better for the series as a whole, too. Annie remaining at Greendale would have been an absolute betrayal of her character, keeping her tied down to a dead-end life with Jeff. Originally, he stayed away from a relationship with her because of her age. But that soon morphed into something much more emotional for him.
The realization Jeff had was that a relationship between them was unlikely to end well for Annie. And he cared about her too much to let her waste her time when she had a real opportunity in front of her. Putting Annie's long-term future ahead of his short-term desires was likely the most selfless thing Jeff did in the entire series and one of the few signs that he had truly grown in any meaningful way.