Achievements are a way of showing a players accomplishments and milestones throughout the game.
Achievements are measured in your performance and growth within Tribal Wars 2. Achievements can be found in different areas of the game. Each achievement gives a number of "Achievement points" that can be seen on every players profile.
Achievement are awarded to you by the game for meeting certain criteria, those could be reaching a specific point level, using the market a number of time or plundering an amount of resources.
The overview page shows you current progress on every achievement category there is. You can see how many point you currently have, and what the maximum number of points are. By pressing on one of the categories, you are taken to the specific category.
This section shows your last 5 achievements. By pressing on one of those you are taken to the specific achievement, with your progress showing.
You can compare your own achievements against another players achievements. This can be done by going to a players profile and pressing compare.
On the top of this screen you see yours (on the left) and your selected players (on the right) achievements points, players points, villages, bashpoints and the actual achievements can be found under the player information.
In the comparing section you have a general overview of which achievements the other players have achieved compared to yourself.