As a particle physicist (no longer working in the field, sadly), this is one of the more exciting results in a long time. Muon g-2 has been there, in some form of another for debate and model building, for many years (taken somewhat seriously for 15+?), waiting for better statistics and confirmation. At over 4 sigma this is much more compelling than it has ever been, and the best potential sign of new (non-Standard Model) physics.
I'm not current on what models people like to explain this result, but it has been factored in (or ignored if you didn't trust it) in particle physics model building and phenomenology for years. This result makes it much more serious and something I imagine all new physics models (say for dark matter or other collider predictions or tensions in data) will be using.
Whether or not anything interesting is predicted, theoretically, from this remains to be seen. I don't know off hand if it signals anything in particular, as the big ideas, like supersymmetry, are a bit removed from current collider experiments and aren't necessarily tied to g-2 if I remember correctly.
re "what models people like to explain": There was some good discussion of lepton universality violation at the end of the announcement talk.
tl;dr - electrons and muons are leptons, but what if they don't interact with photons the same way? (ie the rules of physics aren't universal to all leptons)
I'm not current on what models people like to explain this result, but it has been factored in (or ignored if you didn't trust it) in particle physics model building and phenomenology for years. This result makes it much more serious and something I imagine all new physics models (say for dark matter or other collider predictions or tensions in data) will be using.
Whether or not anything interesting is predicted, theoretically, from this remains to be seen. I don't know off hand if it signals anything in particular, as the big ideas, like supersymmetry, are a bit removed from current collider experiments and aren't necessarily tied to g-2 if I remember correctly.