Proprioception is your sense of where your limbs are oriented in space. It basically means that if you hold your hands or feet in a certain place, you inherently know where they are. You can wave your hands around with your eyes closed and know roughly what position they will be in when you open your eyes.
Proprioception is important for trainers and weight trainers in particular because in order to perform any free weight exercise you need to be aware of where your limbs are and how they are moving. You need to be aware of your limbs in order to correctly perform an exercise with correct form and technique.
If you are a beginner then you will be aware of the issues when trying to perform a new exercise or new motion that feels strange or totally different to what you have done before. If you are an experienced trainer then you will take proprioception for granted. Think back to the first time you did bench press. You couldn’t press the bar straight up and down. It tends to wobble and follow an unusual path up to the top and then back down to the bottom. This is because when you first do an exercise or when you are new to training you have not developed proper proprioception or the proprioception required for that particular movement. The more you perform an exercise or movement pattern, the more you develop the correct awareness of the movement and your limbs to do the exact same movement. This obviously allows you to use correct form and also allows you to perform the movement with more strength as there is no energy loss with controlling the weight as it veers off course. This is one of the reasons why a beginner will gain strength quickly after first starting training (and due to recruitment of motor neurons obviously).
In order to develop proprioceptive awareness you will need to practice a movement a few times. For some it may take longer than others. Simply by performing a movement numerous times your body naturally will be able to follow the same movement without conscious thought or effort. Think about a sport like tennis. The first time you hit a forehand it feels very strange and more often than not the ball will not go in. after a while of hitting the same shot over and over again the movement becomes natural and you don’t even need to think about what your arm is doing as you hit the ball. If you are an advanced athlete in a sport like tennis you will take this for granted. Try playing with your left hand where you haven’t developed this motor pattern and you don’t have as strong proprioception with your left arm and see what happens. I guarantee you will not hit the shot as well as with your right arm, even though you know in your mind how you are supposed to hit the shot.
As you train with weights or do any kind of sport you will become naturally more aware of your body as well. Someone can show me an exercise and I will be able to do it generally after only a couple of attempts due to having well developed proprioception. If you are a beginner it may take far longer to learn the same exercise.
So if you are new to training and feel that you are having a hard time learning exercise technique, don’t let it stop you trying. Keep going with it and you will develop the technique and natural ability to pick up exercise techniques more easily.