Darksiders Genesis has a lot of arcade elements in which you need to jump high enough to reach somewhere. This is required for both secrets and places related to the story.
There are many places in which you have to jump higher to reach another part of a location. These jumps are often problematic - you need to aim at the right spot to go further.
The wings make it easier to maneuver while jumping - you won't fall into the abyss or have problems with jumping to the other side.
Press the right button twice to use the wings (A on the Xbox controller). The character will spread his wings. By holding down the button, you can fly and maneuver the direction of your flight.
Wings will appear only when you are in the air. You can't use them while walking or riding a horse.