Despite its age, AACW remains one of the most detailed and complex grand strategy games out there. Playing a full campaign provides one of the most detailed, micromanagement experiences you can get. This game allows (and requires) careful management of supply lines, chain of command, economy, public opinion, army composition, unit movement, resource management, and information. To name a few.
This game is not for everyone, and people new to AGEOD games will need to be willing to commit several hours going through tutorials and looking stuff up to really understand how the game is meant to be played. There are mini-scenarios that are included with the base game (Gettysburg, Bull Run, etc. campaigns) and extra scenarios that can be downloaded and modded in, which require a lot less micromanagement.
However, the true magic of the game lies in the grand campaign. The payoff to the complexity is unparalleled freedom of choice on the part of the player. You are free to pursue the strategies that you want, and their results are clearly visible on the game map. Unlike many other strategy games, the AI does not need to fall back on cheating. If you pursue a winning strategy and execute it successfully, it will matter.