Like 2.5D games, 2D games can also utilize "depth" by using a perspective camera or utilizing a concept known as parallax, while not having any 3D assets within the environment. To understand the concept of the parallax effect at a more scientific level, let us look at the following diagram:

 

Depending on where you are, certain items are in view instead of others. If a player is at viewpoint 1, then they will see the black circle and blue hexagon; if they are at viewpoint 2 then they will see the black circle and a red hexagon. Moreover, you can also think of it like this as well, when you move within a game space, the "background" that is closest to you moves faster than the "background" that is further away. It is the same when you're driving in an area, such as the country, and you can see the mountains moving slower than the fence. There are many games that use 2D with a perspective camera/parallax effect, such as Braid (featured next).

Other great examples of 2D games that feature parallax environments include Terraria and Limbo.