A corporate bond is a bond issued by a corporation. It is a bond that a corporation issues to raise money in order to expand its business.
A government bond is a bond issued by a national government denominated in the country's own currency that the government uses to raise capital.
Both of them are bonds, so they are both a debt instrument used to raised capital. As far as I can tell, the only real difference is who issues them. However, corporate bonds have a higher risk. As with most things, bigger risk means bigger possible reward. Corporate bond holders are compensated for this risk by receiving a higher yield than government bonds.