PPP (Purchasing Power Parity) is a measure which adjusts the $1.377 trillion for what you can actually buy in India with those US dollars.
It's calculated based on prices paid in India and in Japan or the goods needed to live on; for this reason it's most useful as a measure when looking at per capita incomes to see what a typical person's share of adjusted GDP will buy them. PPP adjusting in theory shows that an Indian in India can enjoy the lifestyle of someone earning three times as much in Japan (provided he buys Indian goods at Indian prices). On the other hand, as soon as you start looking at GDP per capita [adjusted or not] it becomes obvious that Japanese people are on average much, much richer than Indians because Japan's similar level national income is shared between far fewer people.
As an aggregate measure of the economic output PPP adjusted GDP is not entirely useless either as a crude adjustment for labour costs: India can build a lot more skyscrapers for $1.377 trillion (or $1 billion) than Japan could and Indian output is arguably undervalued by raw GDP measures which simply looking at the prices paid. But effectively it's saying that India as a country produces more value than Japan if people were prepared to buy Indian goods at their Japanese value. As there's plenty of opportunity for trade between India and Japan, it's probably fair to say that Indian output probably isn't worth three times it's Indian value to the Japanese, otherwise they'd be buying it all up. Therefore the true value of India's economic output lies somewhere between the $1.4bn at low Indian domestic prices and $4bn at inflated Japanese domestic prices (trade isn't perfectly efficient), still behind Japan.
PPP tends to undervalue infrastructure as it ignores things like subway system when comparing the cost of two condos. Unfortunately it's really hard to value infrastructure as a farmhouse can gain a lot of value from a bridge built 40 miles away. Still, at some level a house is a house is a house even if it’s in a ghetto.
To put it really simplistically : From the perspective of everything within India - PPP is what matters; because it takes into consideration the cost of living. But from the perspective of everything outside India - the absolute figure is what matters.
If we are talking of things from the perspective within India, then it doesn't make sense to compare to Japan? If I'm comparing to Japan, then I'm going outside and I should use the nominal GDP, right?
PPP is only relevant if your typical purchase is similar to that of the basket of goods used to calculate PPP. An iPod or a Toyota will still cost the same - irrespective of PPP - since they are global goods. (In fact due to India's laws they become much costlier in India with around ~30% increase if you convert money.)
True if you consider global goods. But for things that are produced within India PPP is relevant. Then again - it doesn't make sense comparing PPP when you are trying to rank economies on size.
The PPP figure is irrelevant in this case. Purchasing Power Parity GDP figures adjusts the GDP to the cost of living. It has most contextual value when comparing the GDP per capita. PPP GDP per Capita is effectively a metric of the mean wealth relative to cost of living in the country.
To compare total GDP figures on a PPP basis for two countries, and when one country has 10x as many people doesn't really make sense.
What this comparison says is:
(Total GDP of Japan/Cost of Living in Japan) < (Total GDP of India/Cost of Living in India).
The Japanese economy is still 3x bigger (in terms of total GDP), and has 10x higher PPP GDP per capita, or about 30x the GDP per capita.
But there is this "PPP" thing, which turns India GDP to $4 trillion. Which one is more relevant in this case?