So I really feel lost on Quotient groups, I just dont get the concept. My book gives a simple example...

($\displaystyle \mathbb{Z} \oplus \mathbb{Z}$)/ ($\displaystyle \mathbb{Z} \oplus $ <0>)

Could someone explain to me what the construction of this is explicitly and what its structure is?

Im really hoping that I can get the concept with this example. Thanks