Bro Zoossh,
The blackish thing under the baby's eyes is called Kohl in English. In Hindi, its called Kajal.
Check these two links for more details...
http://en.wikipedia.org/wiki/Kohl_(cosmetics)
http://www.gurjari.net/ico/Mystica/html/kajal.htm
Most Indians are a superstitious lot (now, don't flame me on that please. I said
most, not
all). If a baby is beautiful and healthy and others look at the baby and comment "how cute !!! What a healthy baby !!!" etc., the parents think that an 'evil' eye is being cast on the baby. By applying kohl on the rims of the eyelids, it helps ward off the 'evil' eye. Sometimes, its also applied as a big dot either on the side of the forehead or on the cheek.
It is claimed that applying Kohl to the rims of the eyelids has some medicinal value. It acts as a coolant and also helps rid of the germs and dirt etc. that gets into the eyes. I don't know how far its true.
For a list of other popular Indian superstitions, just do a google search and you will find tonnes of them.
Cheers.