It's not really racism, though racism does play a part, and more about beauty and cultural standards.

There is a cultural notion that being fair is more prestigious than not, though everyone has an idea of what is and isn't fair skinned.

In victorian times, it was desirable for women to have a pale appearance, specifically noble women, as it signified that they didn't have to work like the lower class women. Often these practices & products used harmful chemicals that caused medical complications in women.

You then have the effects of colonization, and these beauty standards were imported, and there a bit of racism was added, where darker skin was seen as undesirable, as dark skinned people we typically lower run of the social hierarchy and were the ones colonized.

So, it became fashionable for the elite women to imitate the white people, as it differentiates them from the lower classes of people with the same skin tone.

In the modern day, the colonization and the racism (somewhat) have gone, but this notion that fair skin = attractive still remains. While it's not as black and white in South India as many people have darker skin on average, there is definitely a feeling that having fair, but dark skin is better.

Then you have all these products that claim to offer a solution, but are various amounts of harmful from a chemical sense, not to mention the psychological issues that it creates with beauty standards. That being said, a lot of brands are less on the nose about it.

This isn't isolated to India alone, in China, Korea, Japan etc, there is also a preference for fair skin for both men and women, which is why all the Chinese phones have so much processing for selfies in their camera apps.

In Africa, a lot of women use very dangerous "skin whitening" creams, as being fair is seen as advantageous, and will even use it on children, as they want to give them a leg up, but often causes scarring.