Giving away means spending the wealth and opportunities one has in the way of Allah. In recompense for spending in His way as defined in the verse, "Whatever is surplus to your needs" (Surat al-Baqara: 219), Allah promises this person Paradise in the Hereafter and to compensate for what he gives in this world:
Say: "My Lord expands the provision of any of His servants He wills or restricts it. But anything you expend will be replaced by Him. He is the Best of Providers." (Surah Saba': 39)
… [those who] give of what We have provided for them, secretly and openly, hope for a transaction which will not prove profitless. (Surah Fatir: 29)