Well, there's an interesting history behind it, but before we delve further into it, know that this word has two very different meanings that we found out from this Quora thread and that's exactly what we will discuss in this article.
Apparently, the word 'mall' dates back to the 17th century which essentially means long-sheltered 'walk' or 'promenade'.
In India, this word has been around since the 18th century and is associated with the British era. During that time, a 'Mall Road' acted as a division between married accommodation and living lines road in the military.
So, on one side there used to be Units' living lines along with Unit Admin areas and on the other side, there were accommodations for married British Officers and troops with Bungalows and Messes on one side and lines on the other side.
So, in military terms Mall Road stands for Married Accommodation and Living Line Road. And, each city has a 'Mall Road.'
Though, this word has a different meaning in hill stations.
A 'Mall Road' in a hill station is a place where all major shops and restaurants are located. So, you could say a 'Mall Road' is basically like the city centre which is the most happening area in a hill station or a city.
Shops present in the 'Mall Roads' usually had awnings over the pavement to provide shelter from sun and rain. And, strolling down these roads became a major evening activity for locals and tourists as time passed. Strolling through the busy streets of a mall road is still a popular evening activity in the hill stations.
It is also the place where offices of municipal corporation, fire service and police headquarters are located. And most automobiles, except emergency vehicles, are not allowed on this road
And, while major hill stations still haven't changed the street name/road, things certainly changed a little in the cities post-independence. Most 'Mall Roads' in cities were re-named after famous personalities like Mahatma Gandhi.
Also, let's not forget that in the last 20 years huge 'shopping malls' have replaced old 'Mall Roads' as a destination of choice for strolling and window shopping.
So, now you know why there are 'mall roads' in most hill stations.