The purposes of IRCs is to be able to send someone a letter, along with the cost of postage for them to send you a reply. If the addressee is within the same country, one normally sends them a stamp; but if you are sending a letter to another country, it can be difficult to acquire stamps for that country to send along with your letter. So you can purchase an IRC instead from your local post office, and send it to them; they can then take it to a post office in their own country, and use it to send it back to you. This is often requested when a ham radio operator wishes to send a reception report in order to receive a QSL card - the IRC will cover postage. IRCs can also be used as international currency for small transactions, since they have at least a small nominal value in all UPU member countries.
As well as IRCs administered by the UPU, there are also reply coupons issued by other postal unions available usable only in certain countries, e.g. those issued by the Arab Postal Union.