Achievements are a way to highlight your success. When you get an achievement you also gain a reward of additional money, experience points and fame. There are different levels of achievements; for some of them, you’ll get rare and valuable prizes. That way you have something to strive for!
If you want to look through the list of achievements, select the Administration building and tap the Achievements button at the bottom of the screen.
You can also select the Achievements panel that appears at the bottom of the screen when you get an achievement.