This article is considered accurate for the current version of the game.
Achievements are unlocked for players after reaching certain milestones, achieving hidden goals, or unlocking certain items. There are currently 50 unlockable achievements in Cities: Skylines.
See Global Gameplay Stats – Cities: Skylines at Steam for a list of all achievements sorted by the percentage of players that managed to complete an achievement.
Adding most Steam Workshop modifications will stop Steam from registering achievement completion, though there is a Steam Workshop modification that makes it possible to enable achievements.