Terms like "sense" and "tell" are a bit misleading. It's very much a chemical/mechanical interaction that's automatic. Rather like soap bubbles "sensing" when they've reached the surface of the water.

Plants contain a protein called phototropin, which is activated by light. When it's activated, it changes the shape and alignment of the "skeleton" of the cell, making it more cube-shaped as opposed to long and skinny.

That means the light side of a plant gets shorter, while the dark side remains long. The dark side also grows slightly faster, on a count of having more cells there (you can fit more skinny cells side-by-side than wide cells), and so the plant angles and grows toward the light.