Hm. This appears to be analysis-free, albeit not fact-free. So here goes. Please bear in mind that I am not an economist, I do not play one on TV, and most of the thinking I've done about political economy was in the context of How To Damage Someone's Nation-State (also known as Full-spectrum conflict
The reserve requirement is, at base, just as described above. It is a ratio, and it is imposed on banking institutions and organizations - usually by governments, who have the actual fiat as in fiat money. It is the ratio of deposits to loans that the bank cannot exceed in its dealings. Here is a notional example. If the reserve requirements are twenty percent (that number bears no relation to reality) and if the bank has one million dollars on deposit from those who have placed their money in in the bank, then the bank is allowed to loan out five million dollars to whomever it likes.
See the catch? Wait, you will.
Right! Where did they get the money? They didn't. They made it up out of whole cloth and electrons. Since most banks of the world are no longer on a fixed reserve system (like, say the Gold Standard) this money never really exists except as a concept. For every million dollars in 'actual money' (and yes, actual is flaky here) that people give the bank, that bank will turn around and pump out five million dollars in loans to other people - who will then, in turn, use that money as 'real money' and proceed to spend it, deposit it in other banks, send overseas, etc. etc.
In the old days of the Gold Standard, the reserve requirement was created in order to legally inflate the money supply. This is because in a fixed standard system, backed by hard assets, your economy can't expand faster than you can produce those hard assets. If dollars are always redeemable by gold, then there can only be as much dollars pumped into the system as there is gold dug out of the ground. Well, since bankers are fearfully innovative creatures (and typically far more innovative than the poor bastards who have to regulate them) they swiftly realized that they could accept the risk of a bank run in return for having access to fiat money - by lending out capital at some multiple of the funds they actually had on deposit. This allowed the monetary system to expand faster than the availability of those pesky reserve metals.
However, after the Great Depression (which is just one famous example) the Government - those people with the Fiat, which means guns, or more importantly, tax law - decided enough was enough. The reserve requirement was set up in order to boost public confidence in banks, by ensuring that they couldn't lend out too far past their available assets. Sure, it reined in bank lending to some degree, but it also boosted confidence in the banks - and at the same time, gave the official Government Stamp of Approval to the practice of creating money out of nothing.
In these more modern times, the reserve requirement is simply another tool in the central bank's toolbox, or sometimes in others'. When there is a need for more funds in the economy, the central bank can simply write checks, but that's very visible and inflationary. Sometimes, what is needed is to write some checks but then to ensure that those checks have a multiplier, by jiggering with the reserve requirements.
These days, in most relatively stable countries, the reserve requirements are not only nearly never touched but are often a matter of international agreement, which reflects the increasingly interlocked financial system that those innovative banker types have woven up in their attempts to make money despite pesky regulation.