I quantify this discussion in terms of "labor", but this can be translated into capital, currency or service based on whatever the context of the situation may be. So while discussing usury in terms of interest on currency is the most common, it extends beyond just the idea of currency alone. It's for this reason that referencing everything in terms of labor makes the discussion more universally applicable. It's easy to substitute some other object for labor based on the context and therefore apply the following logic to any situation.
Where does labor come from
We each create our own labor and bring it into the world. We've made the world a better place with our labor and people reward or trade with us their labor. The key here though is that each person is morally owed their labor, nothing more and nothing less. I can't tell someone else that I should be rewarded with some of their labor, that is for them to determine. In the same way, I can't force someone to trade with me, unless they first recognize the value for themselves.
It's important to note here that not all labor is created equal. We each value labor in a subjective manner, varying by numerous factors and virtually impossible to nail down to a single value that would be universal to everyone. All we can be sure of is that if I have my labor wholly intact and in my possession, then I have never been cheated of anything.
Where does interest come from
There are some morally justified reasons to charge others for a loan and then there are some morally unjustified reasons. A morally justified reason would be to restore the damage that was done by the borrower. For example, if I loan someone my car, there will be a certain amount of wear and tear placed onto the car, meaning my labor investment was damaged. When he returns the car to me, then I am justified in charging him for this damage. If by some miracle of nature the car was returned to me without the tiniest amount of damage, then I would be unjustified in charging him for damage. In general people wouldn't think of calling such damage as interest, but rather a fee or service charge, but it's all still the same concept of interest. It's how we trade amongst each other, labor for labor, value for value.
How usury relates to labor
Labor doesn't create itself, it comes from our bodies and also from the workings of nature around us. It's not like if you leave some of your labor alone in a room that it will reproduce itself. We therefore must generate labor for ourselves and then we might trade with others for their labor. However since we're only entitled to our labor, then the extra labor we receive above our own doesn't belong to us.
Interest upon labor is additional labor for the owner of the labor. He gets his original labor back, plus a little bit extra. This is not to say he isn't owed anything for missing labor, but rather that when he has 100% of the labor repayed that he loaned, then the debt is fulfilled.
It's important here to understand that trading labor is a different situation. Since we're not receiving our identical labor back, but rather trading different types of labor, then it's to be expected that there might be differing amounts of labor as a result. So what we're discussing here is receiving back the identical and exact labor that was originally loaned away.
Arguments in favor of interest
People will try to excuse accepting this extra bit of unearned labor (i.e. interest) for various reasons. The two primary arguments used to justify interest are that there is a risk of capital loss for the lender and that there is a time preference for the borrower.
Typically they'll say that there was a risk associated to sharing currency with other people. If this is true, then that is a problem with that particular variety of currency and there are other varieties that exist that avoid this short oming. This shortcoming doesn't justify us getting something for nothing, but is a signal to change currencies.
Others will say that there is a time component to labor, that something shared today is more valuable than something shared tomorrow. This implies that labor diminishes over time. A borrower has an incentive to borrow today, but a lender also has an incentive to lend today as well. If the lender doesn't lend today, then his labor will be diminished tomorrow by the ravages of nature.
Usury proponents will say "currency doesn't diminish over time", so there is no ravages of nature. They say that they might as well hold onto their currency rather than loan it and it will stay safe in their pocket rather than risk losing it to someone else. This is only because of a design feature in the currency itself. Currency is mankinds creation to circumvent the deterioration of labor over time. If this magic of currency didn't exist, then whatever the lender had in his possession for labor (in the form of property) would deteriorate over time. Therefore currency freezes this deterioration over time by artificial means and is just as much to the benefit of the lender as it is the borrower. In other words they both equally benefit.
Why usury is ultimately immoral
Usuray ultimately relies on coercive forces. For someone to unknowingly or even sometimes knowingly enter into a situation where they must borrow with interest, rather than trade, means that they are under some coercive force. Whereas these forces might sometimes be of the borrowers own creation (e.g. greed), it's immoral to participate in something that leads to someone elses moral downfall.
Is it moral to charge interest on someone elses illicit activity in order to dissuade them from doing that activity? Similar to charging a tax on cigarettes or alcohol perhaps. The problem here though is the interest is tainted for the suffering brought into the world. This tainted gain would have to be spent in counterbalancing the suffering that was brought into the world through your assistance. Whatever gain was achieved, was immediately lost and therefore it might have better to never have occured in the first place.