It’s worn so that one of the squares hangs in the front and the other in the back.
There’s a couple reasons behind scapulars. One is that they are a kind of mini-habit–and so they show a kind of spiritual solidarity with the religious order who may wear that habit.
Second, in the middle ages it was a custom for a vassal to wear a cloth of the colors of their lord or lady to show who they were loyal to. This practice was adopted to show loyalty to the Trinity, Christ, Mary, etc. I find it to be a beautiful sign of fidelity.
Third, it can be a little itchy sometimes, so its good penance and a good reminder of Who we belong to.
Finally, to encourage us to wear them, angels, Jesus, Mary, etc. have appeared and offered spiritual benefits besides the usually (for example, Jesus promised an increase in faith, hope, and charity to those who wear the red scapular). Of course, these are private revelations so you can choose to believe them or not. That being said, the Church also offers indulgences for wearing scapulars:
ourladyswarriors.org/indulge/g35.htm