Harish Damodaran, writing for The Indian Express:

When urea is applied to the soil, it is first hydrolysed or broken by water into ammonium ions (NH4+), followed by oxidation to nitrite (NO2-) and, then, nitrate (NO3-) forms. This nitrification process is what makes the nitrogen, which is 46 per cent in urea, available to the crops.

[…]

Neem oil basically acts as a ‘nitrification inhibitor’ when coated on urea. By slowing down urea hydrolysis and nitrification, it allows a more gradual release of nitrogen, which can be used by the plant. “Neem-coating increases nitrogen use efficiency. Also, since the urea action is prolonged, the plants stay greener for a longer time. Farmers apply urea when they notice the leaves turning yellowish. But if the crop here is retaining greenness for an extended period, they would reduce the frequency of application. Instead of three bags for an acre of paddy or wheat, they might be using only two now”, Prasad points out.

Some science behind the ‘magic’ behind neem-coated urea, which might explain the contradiction that although food grain output is rising YoY, fertilizer sales are in fact, down, including that of urea. Good read.