What does 'currency convertibility' mean? As a student with almost zero background in economics, I've been struggling to comprehend the notion of the currency convertibility. Most of the definitons I've found online talk about the ease with which a country's currency can be converted into another currency. But what exactly is meant by the ease? Does it mean both currencies should be equal, or close to being equal, in their value or is it something else?  

To provide context, I'm attaching the part of an article from nationalarchives.gov.uk talking about the American financial aid to Britain during and after the WWII. Also, as I'm not able to figure out the meaning of the word, I don't understand the following (the last) sentence of the extract either.


  The economic circumstances of the late 1940s tested relations between
  the unions and the Labour Party. Financial assistance through the
  American lend-lease system ended in the autumn of 1945. Although a
  further loan was negotiated in 1945, it was apparent that a great
  increase in production and exports would be necessary to prevent a
  balance of payments deficit. In the winter of 1947, a coal shortage
  produced an energy crisis, which threatened to undermine production.
  
  In July 1947, the Chancellor, Hugh Dalton, returned the pound to
  convertibility against the dollar (as required by the terms of the
  American loan). However, as dollar reserves rapidly flowed out of the
  country, a full-blown economic crisis followed and in August of the
  same year Dalton was forced to suspend the move.


Thank you in advance for the response, I'd very much appreciate it.
This definition of a freely convertible currency may be clearer to you:


  Freely convertible currencies (also called as fully convertible or permitted currencies) are those that anyone can convert into another foreign currency without restrictions or interventions by government of the original country.


It makes clear that the "ease" you refer to typically refers to the lack of government restrictions.

The stereotypical case of a non-convertible currency is one for which the government maintains a fixed exchange rate.  Imagine the UK pegs £1 to be worth \$2, although the market value (i.e. the equilibrium if restrictions were lifted and the goverment didn't intervene) is only \$1.80, say.  In order to maintain this exchange rate, the UK government has to be willing to buy sterling for a price of \$2 from anybody that wants to sell it.

Often this leads fairly quickly to the UK government running short of dollars, at which point the temptation is to try to bring in some sort of restrictions on who can buy dollars, in what circumstances, how long they have to wait for them to be delivered, etc. -- in order to slow the outflow of foreign exchange.  They may also introduce laws that say that when British firms sell goods abroad, they have to convert the dollars they earn to sterling through the central bank, to provide a bigger source of foreign exchange.  They may also introduce laws banning the conversion of pounds by banks, street traders, etc.

By this point the "ease" with which sterling can be converted is pretty low; it has low convertability.

In the example you mention, the UK suddenly removes restrictions, returns the pound to full convertability, and buys dollars from anybody that wants to sell.  In this situation, you'd expect all sorts of people to rush to buy dollars from the UK government at the favourable rate before they run out and are forced to reintroduce restrictions.