As a dancer you are highly prone to injuries. You are constantly forcing your body to do things that are quite unnatural. If you are not wearing well-suited poitne shoes, over stretching or not stretching enough, not receiving proper training, etc. you can potentailly damage your body.
Injuries not only are painful, but they also come along with consequences. For example, the pointe shoes I had previously been wearing had causing me to accumulate multiple stress fractures in my feet. Being injured caused me MANY weeks without dancing, and also diminished a few large opportunities. The worst case scenarios of getting injuries are A) You basically start again from square one of your training after you have healed, or B) You can never dance again.
In order to avoid injuries, there are quite a few things you can do. You can stretch, and sometimes hesitate stretching (shocker!), you can take hot baths, you can take cold baths, you can put your feet in bucket of a mixture of water and ice for 10 – 15 minutes. If you fear you might be injured or are becoming injured there is always the option of visiting a doctor. Some people might suggest using creams like ICY-HOT or even take medicine and vitamins. Also, if you trust your instructor's judgment you can always go to them for their input or advice.
In short, injuries should most definitely be a concern for all dancers. There are many ways to avoid and care for injuries, but they will always remain a risk factor can concern in a dancer's life.