Why an automobile’s windscreen glass shatters into rounded pieces when it breaks?

It is because this particular type of glass has undergone the process of toughening or lamination. Automobile windscreen and aircraft windshields must withstand severe impacts without shattering. The kind of special glass used for such purposes is called safety glass. It is far stronger than ordinary glass and does not shatter into sharp, dangerous splinters.
Two main kinds of safety glass are produced—toughened and laminated glass. Toughened glass is made by  heating glass sheet in a furnace. It has its temperature uniformly raised until it is just beginning to become plastic. It is then quickly lifted out of the furnace, bent where necessary between matching tools and then cooled rapidly and uniformly all over by jets of cold air blown forcibly on to it. This process is called tempering. When toughened glass breaks, it shatters into hundreds of blunt, rounded particles which cannot cause bad cuts. 
Laminated glass is a kind of glass and plastic sandwich. Two sheets of flat glass with a layer of polyvinyl butyral in between are gently heated under vacuum which evacuates all air from the laminates and is then heated to bonding temperature under pressure. Laminated glass is safe because when it breaks the pieces of glass stick to the sandwiched layer of plastic.

Additional reading:
Toughened glass (Wikipedia)
Laminated glass (Wikipedia)

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