To anybody who's vaguely knowledgeable about these things, it not only points out my nationality, but also which region of India I belong to, my religion, and also my caste[0].
[0] Not that I pay attention to caste, but as you can see, Indian surnames contain a lot if information, to anybody even remotely trained in reading them.
Beyond that's, it's a Hindu name. Almost all Hindu names are specific to a particular caste (the origins of the caste system are simply a precise codification of socioeconomic status, so it's similar to someone being called "a Trump" or "a Kennedy").
Priests can also tell further information from the name, such as the gotra: http://en.wikipedia.org/wiki/Gotra . In layman's terms, this is a way of identifying one of your earliest known ancestors.
The name even has a Wikipedia page: http://en.wikipedia.org/wiki/Mukherjee
[0] The British changed a lot of names of both people and places when they were in power - ex., they changed "Mumbai" to "Bombay", although people are now starting to use the original name again.