Yes, with an AR component, a shock/innovation/whatever you want to call it, positive or negative, will have persistence in your model. It means that if sales were higher yesterday, they will, on average, tend to be higher tomorrow.
“Innovations” is just time series jargon for exogenous shocks. You can do fancier stuff to explicitly model them as correlated errors, but for AR it works out to be the same as just including lags of sales as a little regression.
The more variables you bring in that might explain exogenous movements, the better. It’s hard to give suggestions here without domain knowledge, but calendar effects are a good place to start looking. The only downside to including exogenous variables is that it makes forecasting difficult, but that doesn’t seem to be your objective here, so go nuts.