Convertibility can be related as the extent to which a country's regulations allow free flow of money into and outside the country.
For instance, in the case of India till 1990, one had to get permission from the Government or RBI as the case may be to procure foreign currency, say US Dollars, for any purpose. Be it import of raw material, travel abroad, procuring books or paying fees for a ward that pursues higher studies abroad. Similarly, any exporter who exports goods or services and brings foreign currency into the country has to surrender the foreign exchange to RBI and get it converted at a rate pre-determined by RBI.
After liberalization began in 1991, the government eased the movement of foreign currency on trade account. I.e. exporters and importers were allowed to buy and sell foreign currency, as long as the items that they are exporting and importing were not in the banned list. They need not get permission on a CASE TO CASE basis as was prevalent in the earlier regime. This was the first concrete step the economy took towards making our currency convertible on trade account.
In the next two to three years, government liberalized the flow of foreign exchange to include items like amount of foreign currency that can be procured for purposes like travel abroad, studying abroad, engaging the services of foreign consultants etc. This set the first step towards getting our currency convertible on the current account. What it means is that people are allowed to have access to foreign currency for buying a whole range of consumable products and services. These relaxations coincided with the liberalization on the industry and commerce front - which is why we have Honda City cars, Mars chocolate bars and Bacardi in India.
There was also simultaneous relaxation on the restriction on the funds that foreign investors can bring into India to invest in companies and the stock market in the country. This step led to partial