I am trying to include some extra stretching in my workout routine so I was looking at some Youtube videos and blog articles about it. However, a lot of people say you must do stretching in order to avoid "injuries". I am confused about what do people actually mean by injuries in those resources. Are they referring to avoiding sore muscles you tend to get after gym or actual injuries, such as dropping a heavy barbell on your foot?
I would have to see the videos in question, but I suspect that most of the time they are talking about stretching to increase the range of motion. For the vast majority of the general public, this isn't going to be a problem as "normal" day to day flexibility should be more than sufficient for basic fitness and lifting routines.
If, however, you have pre-existing deficiencies in your range of motion, or previous injuries then stretching may help you complete the exercise safely. There is no real way to assess this, however, without a visual examination by someone (such as a physical trainer) that can diagnose that sort of thing.
Stretching has been studied somewhat off and on, and to date, there are no definitive studies that say yes or no, stretching prevents injuries.
"Injury" in the context of weightlifting typically refers to repetitive strain injuries. Lifting heavy weights is meant to stress the muscles, but too much stress (high weight or not enough recovery) can cause a muscle to tear. Heavy weights also strain the tendons and joints. You could encounter knee pain due to an overused patellar tendon, or shoulder pain due to undertrained muscles not being able to stabilize the joint under heavy loads. Poor form also causes injuries. Failure to maintain a neutral spine can cause the discs in the spine to squeeze out from between the vertebrae causing various pains.
Stretching is an attempt to prevent injuries caused by poor form, when joints can't move into the proper position for a lift. If the joints can't move because of other issues, like the brain having gotten into the habit of not using the muscle that is supposed to extend that joint, then stretching won't help.
A lot of people are saying otherwise too. The important distinction is the difference between flexibility and mobility. People think flexibility is important, but it is actually inferior to mobility.
I would recommend you to look at Kelly Starrett's videos and talks; also he has a very good book about mobility which is called Becoming a Supple Leopard.
Lastly, it is never a good idea to stretch cold muscles. If you want to do stretching, please do a light warmup before hand, and choose dynamic stretching over static stretching.
Overall, the most important thing is doing full range of motions, without using any momentum in your training.