Crocodile breath is a yoga exercise or technique for teaching and training diaphragmatic breathing. It is perhaps the easiest means of doing this that I have come across.
To begin you lie on the floor (prone or face down) with your forehead on the back of your hands - neck is in alignment with the rest of your spine - this is a relaxed position. Then you will breath in through your nose and deep into your "belly" - when you do this correctly you will feel your stomach push out into the ground and your obliques will push out to the sides as well - your lower back may even rise and fall with your inhale and exhale. Once you have a comfortable inhale you simply exhale and begin again.
Do not be in a rush. Let your breathing come at a natural pace and be sure to feel the stomach push out into the floor.
Build up to being able to perform the "crocodile" breath for 5 minutes and you will have gone a long way towards retraining your breathing and having a great feel for what it means to breath with your diaphragm. Another benefit of this style of breathing is that you will mobilize your thoracic spine and when your thoracic spine can move well - your shoulder will move and function better. The diaphragm and intercostal muscles are integral to the proper functioning of your body - shoulder included.
Enjoy this "exercise" and the benefits it can bring.