CrossFitters hate to stretch. There is no competitive stretch time or 15 min AMRAPs of back bends (though that sounds like an interesting idea). If you are not already flexible stretching is uncomfortable and humbling in one awful package. Most people avoid stretching, but flexibility is an important aspect of your physical fitness especially if you are doing something as demanding as CrossFit.
Stretching Can Help You Avoid Injury:
Flexibility allows you a greater range of motion (ROM), and you know that ROM is enforced seriously in CrossFit. When you are inflexible full ROM is harder to achieve and you compensate with other muscles and joints to get into difficult positions (like the OHS). Usually, the muscles and joints that are secondarily recruited are not as suited to the movement and can more easily become overloaded leading to injury. Even in everyday life, flexible muscles are easier on your joints allowing proper posture and positioning- less wear and tear in general.
Stretching Makes You Stronger:
Stretching does not make you stronger the way a 3X5 set done consistently with increasing weight, but it does have a great deal of effect on strength indirectly. If muscles are inflexible, you can consider them pre-loaded. For example, tight hamstrings are already loaded with weight from the tension of pulling against your own body that you cannot recruit them 100% in your back squat. Every stiff, tight muscle takes away from the force you can use to perform athletic movements.
It is important to stretch before and after the workouts, and everyone should dedicate some time each week to really work on flexibility so that the ROM for athletic and daily movements can be achieved with ease.
The kind of stretching you do is important also. Before a workout, you should only be performing dynamic stretches (stretches held for a few seconds with motion in between- we do these often). You can also use the Mobility WOD tricks for increasing ROM (not stretching exactly, but used with a good warm up, dynamic stretching it can really increase your performance that day). Static stretches before lifting especially reduce the efficiency of contraction; save these stretches until after your workout, as you will be weaker for a few hours after intense static stretching.