Let’s see the difference of white balance with this photo.

I changed the white balance using WARMTH function on Instagram and made two photos: cold one (bluish one) and warm one (reddish one). The cold one, the original and warm one from the left to right

Look! The colors of young lady’s skin tone, coat, scarf and hair are different.
Let us make it clearer. Please see the photo below. I removed colors of each photo. So you can see what WARMTH had done on these photos.

Can you see the difference of above gray images? The gray scale image shows the 0% – 100% level of white. The function definitely changed the white. The balance of Red, Green and Blue light had been changed.
All the colors are expressed by the combination of Red, Green and Blue light. If you change white to reddish white, almost all cases, Red light you can see becomes stronger and white and the other colors also become reddish.
For your info
Digital Camera captures Red, Green and Blue data. Professional photographers take photos and edit Red, Green and Blue data (RAW data) directly if White Balance needs to be changed.

Usually, ordinary people do not know how to edit Red, Green and Blue data. It is very complicated.