For e.g. say a circular 2D entity and we pass our finger through a paper, they would just see a circle forming with increasing diameter till its circumference is equal to that of our finger and then when we take our hand off, this circle would reduce in size and then vanish.
You(a 3D entity) can touch the center of the circle(2D entity) without breaking its edges. In a similar way, maybe a 4D entity could touch our inner organs without cutting us open.
The movie "Flatland" portrays this concept really well of 2D entities interacting with a 3D entity.
This can be supplemented with further reading about the allegory of "Plato's cave".