Sarah Connor, and her journey from normal working stiff trying to make her way in the world to badass defender of mankind. Sarah goes though a lot, and Hamilton plays every bit of it with the proper emotion, or in some cases lack thereof.
While Terminator 3 was a box office hit, and received generally positive reviews from critics, it's always kind of sat in the middle for most diehard Terminator franchise fans. It's leagues better than Salvation and Genisys, and more fun than the often downbeat Dark Fate. Yet, it's also clearly not on the same level of the classic first two films directed by James Cameron. It's worth watching, but it's not a truly great film.
Part of the reason Terminator 3 doesn't ascend to those heights is probably the absence of Sarah Connor, as well as Linda Hamilton didn't come back.
Terminator 3: Why Linda Hamilton Didn't Return as Sarah Connor
Back when Terminator 2: Judgment Day, she still felt that without her ex-husband at the helm, Terminator 3 would be DOA. At that point, Edward Furlong was still set to reprise John, although he would eventually get fired due to drug problems.
In a 2009 interview, Hamilton expanded on her reasoning for not being a part of Terminator 3, saying that she read the script but was unimpressed. Hamilton felt her character arc had been done perfectly in the first two films, and didn't want to bring Sarah back without good reason. The script she was given shifted Sarah to the background of the story in favor of focusing on John, and killed her off halfway through, with no time taken to mourn her death. Hamilton felt the script made Sarah a disposable character, so she declined the offer to return, and Terminator 3 was changed so that Sarah had died years before. Thankfully, Terminator: Dark Fate eventually provided a real opportunity for Hamilton's Sarah to be resurrected, placing her at the center of the story.