If you shoulder some object, like a backpack, you put it onto one or both of your shoulders and carry it. You might shoulder your backpack, or shoulder a bucket of water, or even shoulder your little sibling. This dad is shouldering one kid and holding the other two in his arms:
If you shoulder some duty, burden, or responsibility, you "carry" it, meaning you deal with it and take care of it, even though it’s difficult. Sometimes, if people expect you to take care of a LOT of things, it can feel like the whole world is on your shoulders.
So that's one common meaning of "shoulder." Here's another. You can shoulder into or through a place, or shoulder your way somewhere, meaning you push your way through with your shoulders. This might be because you’re walking into a strong wind, or because there’s a lot of other people that you have to shove through.