What is Riba according to the Quran? Please also state the verses in the Quran that hints to the term.
There is no clear-cut definition of what riba is in the Qur'an. The understanding based on the reading of verses is that, it is some form of an increase in a loan, that might end up doubling or quadrupling the debt, and that it is not to be confused with trade/sale. The aHadith are where you will find a more detailed explanation of the term.
There are four places in the Qur'an where Allah mentions usury:
[Surat al-Baqarah 2:275-76, 278-79] Those who swallow down usury cannot arise except as one whom the Shaytan has prostrated by (his) touch does rise. That is because they say: Trading is only like usury, while Allah has allowed trading and forbidden usury. To whomsoever then the admonition has come from his Lord, then he desists, he shall have what has already passed, and his affair is in the hands of Allah; and whoever returns (to it) - these are the inmates of the fire; they shall abide in it.
Allah does not bless usury, and He causes charitable deeds to prosper, and Allah does not love any ungrateful sinner.
O you who believe! Be careful of (your duty to) Allah and relinquish what remains (due) from usury, if you are believers.
But if you do (it) not, then be apprised of war from Allah and His Messenger; and if you repent, then you shall have your capital; neither shall you make (the debtor) suffer loss, nor shall you be made to suffer loss.
[Surah Ali `Imran 3:130] O you who believe! Do not devour usury, making it double and redouble, and be careful of (your duty to) Allah, that you may be successful.
[Surat al-Nisaa' 4:161] And for their taking usury though indeed they were forbidden it and for their devouring the property of people falsely, and We have prepared for the unbelievers from among them a painful chastisement.
[Surat al-Rum 30:39] And whatever you lay out as usury, so that it may increase in the property of men, it shall not increase with Allah; and whatever you give in charity, desiring Allah's pleasure - it is these (persons) that shall get manifold.
Riba, translated as interest or usury, is strongly forbidden in Islam to the extent that there is a declaration of war from God and His Messenger against the one who practices it (Holy Qur'an 2:278,279).
However, the concept of Riba is a lot wider than is commonly understood. The term Riba need not be restricted to any amount charged on cash, but can also mean any kind of excess given over and above any commodity. So any excess paid by a borrower of, say, wheat, to a creditor also implies riba.
If you think a little harder, riba is an anomalous charge that creates absurd situations in society. To take an instance, most nations today have central reserve banks (like the Fed in the United States) that retains the sole right to print currency. It then loans out these monies to banks with the understanding that the latter will return the same amount + interest on these monies. But since the central bank itself retains the right to create currency, there is no way that the banks will be able to return the interest amount except by getting it by fair means or fowl from the other banks (and the consumers). This fact itself is a losing proposition for any society that has a central bank as such.
I think there's another way to look at it, especially if you look at the principles mentioned throughout the Quran.
Riba meaning Increase
If you think about equity, justice, fairness mentioned throughout, it would suggest that it's not fair to increase one's wealth without some 'active work'. As phoenix mentioned in his quotes if I deposit some money and make a profit without putting effort in then it's obviously unfair. However if I make a loan to someone with the intention to make a profit based on some risk I've taken (of default), and analysis of the business etc, then I'm making effort and I will be duly recompensated.
That can then be applied much more widely to any kind of work. Wherever there is (free) reward without a risk then it's an increase in wealth without justification.