how was 1991 a year of important changes in the history of the world and of India
Answers
1991 was an year of some big & dramatic events in India as well as internationally which turned the course of history.
International events first.
Dissolution of USSR [1] :
For so many decades, Union of Soviet Socialist Republic (USSR) was a powerful entity in the world.
After the end of World War II, the whole world was divided into 2 parts - US aligned or Capitalist nations and USSR aligned or Communist/Socialist nations.
World has seen Cuban-crisis, cold-war and nuclear threat because of conflicts between USA & USSR.
Collapse of USSR was a big event which shook the whole world. Fall of USSR meant fall of Communism/ Socialism ideologies.
Eastern European countries rejected the leftist mindset and started a new journey in 1991.

First Gulf War [2]
In 1990, Iraq attacked its neighbor Kuwait for control over its oil fields.
Iraqi president Saddam Hussain was quite confident of his republican guards army who were seasoned after the 8 years war with Iran.
Saddam was proud of his army and scud missiles which were able to bring damage to neighboring countries.
Gulf war 1 was the first time event in world history where a war was seen on a live TV.
People were amazed to see air-strikes in Iraq.
https://www.youtube.com/watch?v=kttGXkh_Zi8
They saw the launch of Scud missiles and counter-attack of Patriot missiles in Tel Aviv.

This was the first time, world was watching modern weapons like laser-guided bombs, Tomahawk cruise missiles, planes like Blackbird

War and Collapse of Yugoslavia[3]
Yugoslavia in 1991 was a republic comprised of regions like - Slovenia, Croatia, Bosnia-Hercegovina and Serbia.

There has been a tension between ethnic groups of Serbia, Croatia & Slovenia after the fall of communism in 1990s.
World saw Ten-Day War in Yugoslavia followed by Croatian war, Bosnian war and Kosovo war in which thousands of people lost their lives.
Change of name of a city thrice in the same century[4]
Yes, it is St. Petersburg.
In 1914, after Russian revolution, Bolsheviks changed the name from St. Petersburg to Petrograd.
In 1924, after the death of Lenin, the name was changed to Leningrad.
In 1991, we saw the city was renamed St. Petersburg.
Some Important Indian events -
Assassination of Rajiv Gandhi[5]
On 21st May 1991, India was stunned listening to the news of assassination of Ex-PM, Rajiv Gandhi.

This is the last photo of Rajiv Gandhi before his assassination.
The girl seen with orange flowers in hair is Dhanu, a suicide bomber who was associated with LTTE.
She went near to Rajiv Gandhi and detonated a bomb tucked below her dress.
LTTE feared that, Rajiv Gandhi if come back to power, will again resend the IPKF to Sri Lanka.
LTTE didn’t want to take any chance, so they planned and executed this project to eliminate Rajiv Gandhi.
Indian economic crisis of 1991[6]
By the end of 1990, Indian economic system crippled, fiscal deficit has increased and things get worse with start of first gulf war.
The condition got so bad that Indian government had to airlift national gold reserves to IMF as a guarantee to pay the pending loans.
P.V. Narasimha Rao took charge as PM of India and alongwith Finance minister Manmohan Singh introduced several reforms which are part of his liberalization/ globalization policies to open the doors of Indian market for world industries.
It was only after 1991, we saw an economic boom in Indian industry.
Thanks for reading!
Footnotes
[1] Dissolution of the Soviet Union - Wikipedia
[2] Gulf War - Wikipedia
[3] Yugoslav Wars - Wikipedia
[4] Saint Petersburg - Wikipedia
[5] Assassination of Rajiv Gandhi - Wikipedia
[6] 1991 Indian economic crisis - Wikipedia