Why an imported Chinese product in India is cheaper compared to a locally manufactured item?
Consider an exact same product, say an umbrella, which is both imported from China in India and locally produced. The reason why the Chinese product is cheaper compared to the local one could be related to differences in productivity or total factor productivity. The Chinese product could be relatively cheaper because Chinese firms use better production techniques, higher-quality general labor and capital input, better managerial practice/talent, or better information technology. See the JEL survey about What Determines Productivity?
The recent paper by Rodrik and co-authors documents that labor productivity is higher in China than in India (see Table 1). This could be a first reason why prices of the same product differ.
The cost of the umbrella is the sum of the cost of input raw resources (wood / plastics / metal / fabric), labor, transport and retail. Assuming the retail costs are the same (you're buying in the same store, for example), then the difference is on the other factors.
Keep in mind that the cost of all the factors can be manipulated by the Chinese and Indian currency. Given that China probably owns all the resources needed for the production of the umbrella, they can produce it all and export it at a low price by devaluating their currency, lowering the total production cost of the umbrella. This will make China's exports cheaper and imports more expensive.
Without a specific case, we can't give you a more specific answer, but hope it helps!