If a currency, e.g. the rupee (INR), is appreciating against, say, the USD, it possibly means that there is a high demand for the former. India could have net exports, high remittances, increasing FIIs all leading to the appreciation of the INR. Does that not mean a lot of rupees flowing into circulation in the country? Should that not decrease the value of the currency and lead to inflation? Where exactly am I wrong?
You are wrong/vague here:
the rupee (INR), is appreciating against, say, the USD, it possibly means that there is a high demand for the former.
If the rupee becomes more expensive w.r.t. the dollar, demand for the rupee usually decreases, as Indian exports are now more expensive to pay for when measured in dollars, and hence fewer people seek to convert their dollars to rupees to pay for these exports.
" Does that not mean a lot of rupees flowing into circulation in the country?" no. it means other currencies are flowing into the country, eg USD. then locals will go to their banks and exchange USD for RUPEE. There will be no new RUPEES created (unless the crazy scenario of all the banks run out rupee and them needing the central bank to print more rupee!).
note that indeed ultimately you could argue that there is more rupees "in circulation".
and so if the indian economy starts to grow really strongly due to exports, and the fx value of the Rupee starts appreciating, then if you get to a point where real resources start to become scarce, and demand exceeds supply, then certainly you can get inflation, as thats what you get when the economy tries to grow beyond its real resource limits.