Short answer
Because light bounces between the walls. Each wall reflects coloured light onto the others, so the colour you see is the paint plus several bounces of itself — which deepens and intensifies it. A small card, surrounded by white and held near a window, receives none of that, which is why it always looks lighter than the finished room.
This is inter-reflection, and it compounds with saturation. A near-white wall reflects light that is still near-white, so the effect is small. A mid-toned or saturated colour reflects light of its own colour onto every other surface, and those surfaces reflect it back, so the room converges on a deeper, more saturated version of the chosen colour. The effect is strongest in small rooms, where the walls are close together and each bounce is less attenuated.
For anything beyond a pale neutral, assume the finished room will read a step deeper and a step more saturated than the sample did.
The smaller the room, the stronger the inter-reflection. A colour that is right in a large room is frequently one step too strong in a small one.
Two sample boards on facing walls give you a hint of the effect that one board cannot, because you can see how each reads against the other.
Artificial light adds its own colour to every bounce, which is why a room can shift character completely after dark.
Use saturated colours carefully in small rooms with limited natural light. The colour is not the problem — the combination of inter-reflection and low light is, and it can turn a rich mid-tone into something considerably heavier than intended.
How to test it
Put boards on two facing walls and stand between them. It is a crude approximation of the finished effect, but it is far closer than a single board and it takes no longer.
Undertone
Inter-reflection amplifies undertone as well as depth. A wall colour with a faint green cast can make the whole room read distinctly green once all four walls carry it, even though the cast was barely detectable on the sample.
Lighting
The effect is different in a bright room and a dark one. In a room with little light, the extra depth from inter-reflection is not compensated for by direct light, and a mid-tone can end up reading as a dark colour.
Finish
Higher-sheen finishes reflect more of the surrounding room, which strengthens inter-reflection further — a satin wall in a saturated colour will pick up and throw back more colour than the same colour in matt.
Whatever a calculation or a chart says, view a physical sample in the actual location before committing to a large surface.
Colourwise editorial guidance, drawn from conventional decorating practice and from the physical behaviour of light and surfaces described in the linked lighting and finish guides. Not manufacturer advice — always follow the specific instructions supplied with any product you use.