1) Incredible Action to raise the stakes.
When it comes to making action better in a sequel, there is absolutely no one better than James Caameron. Before he started going downhill after Titanic, James Cameron was widely known for using great action and used it to raise the stakes in his films. As much as the action in Terminator was cool, it wasn't the main draw of the film. The Original film focused on its story more on the horror aspect of Arnold's character because, after all, a killer robot played by Mr. Freeze from Batman and Robin (with no funny puns) was coming to kill you is pretty terrifying. Here, the film has elements of horror, but is purely highlighted and starred by the action. There action chases, gun play, fist fighting, and big set pieces that were awesome, entertaining, and kept you on the edge of your seat. It had to raise the stakes, and boy did it do so.
2) The T-1000
Alright, I'm going to get major heat for this, but I wasn't the biggest fan of Arnold as the original T-800. I mean he was good, but it was clearly evident from the moment we saw him that he was the bad guy. Here, this film takes it in a more fresh, and more creative direction with the T-1000. Played by Robert Patrick, the T-1000 was both badass and also terrifying, This was the original unkillable badass before Deadpool, as he could just come back from anything thrown at him. This was someone that could turn into anyone, anything, or any sharp, stabbing weapon that he wanted, He took everyting thrown at him til the very end, and could be anyone, which just made him even more terrifying. He was there to kill John Connor, and wouldn't stop until he suceeded and his mission was complete.
3) Sarah Connor
Speaking of things that I wasn't the biggest fan of from the original Terminator, Sarah Connor was just okay in that movie. She wasn't bad, she was just the ordinary damsel that we've seen a hundred times. This film went in the best direction possible and made her into one of the best female characters in film history. We see what the first film put her through and how much she is trying to save her son and the world from destruction, only to have no one believe her and call her insane. She becomes hardened, toughens up, and is turned into the best action character since Ripley in the alien movies (thanks again to James Cameron for Aliens). We see how she had to change herself in order to survive, but also remain the good woman we remember Sarah being and loving to her son, as she remembers her son and her humanity. Badass, kind, and complex, Sarah Connor was the best overall package.