I would say that in order to create a meaningful choice in a game it has to impact either the gameplay in some considerable and tangible way or the world that you are currently inhabiting or characters within that world.
An example of meaningful choice in gameplay would be class or skill selection in an RPG. This choice would impact the way you interact with the world. It would cause you to play in a certain way. Throughout the entire game this choice will stick with you.
When it comes to changing the world or characters within it this can be much harder. Some games will have choices that do not impact the world much. An example of this is you make a decision within some dialogue and now a character will just vanish without any ties to the story or just have a new hat. This doesn't help with your connection to the world or story. You want to feel connected to your choice and see its widespread impact in the world or with a character. An example of this would be allocating your forces in a large war. You have a certain number of units. You cannot help everyone. You have interacted with all of these towns and built relationships with them. Who do you decide to help. Someone will die that you have known.