How is a country's interest rate and inflation linked? India has just dropped its lending rates. Is the drop in interest rates linked to the country's inflation?

Link to article - http://in.reuters.com/article/2015/09/14/india-economy-inflation-idINKCN0RE04V20150914
You're probably not looking for a complex scientifical discussion on the subject, so here's a very simplified description of the mechanism:

Lower interest rate => Loaning money is cheaper => More money in the system => Higher inflation.

So the change in inflation is one of the products of government/central bank changing interest rates.