Everything that happens on the campaign strategy map has ramifications on the battle map and vice versa. For example, if you ambush Hannibal crossing the Alps, your legions will be forced to fight in snowy, mountainous terrain, and likely suffer for it. Likewise, if you lay siege to a city, burning the buildings during battle, you'll need to rebuild those charred remains afterwards.
The subtle genius of Rome is the excellent balance between grand strategy and front line tactics. Don’t care for diplomacy, taxation or construction? Simply let the competent AI handle that for you in select cities; or have it run your entire empire automatically. On the other hand, if you find yourself getting bogged down in the combat zone, you can auto-resolve conflicts there, too, but at greater risk of losing by not being directly involved.