An appeal can be made to a ruling by the Judge. In this case, Judge Chutkan ruled that Trump did not have presidential immunity when he took the actions he is accused of taking. He was still POTUS at the time of all the actions. The Presidential Immunity would preclude him from any lawsuits for actions taken while POTUS. So Trump appealed that ruling. The issue is whether presidential immunity applies in this case.
Now it gets squirrelly. Trump didn’t appeal to the SCOTUS…Smith did. Trump appealed to the appellate court as is normal for appeals. Smith didn’t want to wait for the appeals process to work its way through. He is pushing a timeline that would impact Trump’s ability to run for POTUS again. It is all political. If the appeal went the normal course, the appeals court would take time for the case to get up to the top of the pile, time for them to review all the materials pertinent to the case, time to mull it over and time to make a ruling. All that could take months. Because of the nature of the appeal, the entire case is on hold until it is ruled on and the appeal is settled. If the appeals court rules in Trump’s favor the case is tossed out unless Smith wants to appeal to the SCOTUS. If the appeals court rules in Smith’s favor the case can continue, picking up where it left off but Smith’s accelerated timeline is still screwed. Also if they rule in Smith’s favor then Trump can appeal to the SCOTUS which will further delay things.
So Smith went right to the SCOTUS in an effort to speed things along. Unfortunately for him, the SCOTUS usually relies heavily on the ruling of the Appellate court when looking at the issue. They look at the issue, they look at the how and why the appellate court ruled a certain way and then they review and interpret the law. Without the appeals being heard by a lower court, the SCOTUS is reluctant to hear the case, effectively pushing Smith back to the Appeals court process.
None of this is anything that Trump did wrong. He did exactly what any defendant would do. It was Smith that tried circumventing the process to keep a timeline that seems more and more to be designed for political reasons.