The camera reckons that the scene is an average Grey (18% grey was the standard but with digital 12% grey is often used)
If the scene is lighter than the average Grey, as snow would be, the camera thinks that it is an average scene on a bright day so it reduces the exposure to make the snow average Grey. You need to overexpose to compensate.
If you are photographing something black, an animal for example, the camera thinks that it is an average scene on a dull day so it increases the exposure to make the black animal average Grey. You need to underexpose to compensate.
More problems can arise because of the "intelligent" cameras we now have, some of them actually compare the meter output with readings in their memory and adjust the final reading accordingly.
In the old film days I used a seperate meter to take incident light readings where you metered the light source and not the subject, it did not matter if the subject was white, black or anything in between. The light from the source is what matters. Because we now meter the reflected light we have to compensate for whatever is doing the reflecting.
Worth repeating - The light from the source is what matters, if you think about that and understand it you will realise why compensation is needed.
Do this at home

Put the camera on Auto and take a picture of just a white card (fill the viewfinder with the card), then in the same lighting take a picture of just a black card, in post processing convert both to B&W (to get rid of any colour casts) and see what you get.