What was Operation Desert Storm (1991)?

The US-led attack to free Kuwait

What reason was given for invading Iraq in 2003?

Claims that Saddam had weapons of mass destruction

Saddam Hussein's Iraq invaded Kuwait in August 1990, partly over oil and debts. The UN demanded Iraq leave.
A US-led coalition, including Britain, attacked in Operation Desert Storm (January–February 1991) and freed Kuwait. Saddam stayed in power and crushed uprisings; no-fly zones followed.

The Taliban took Kabul in 1996 and gave shelter to al-Qaeda and Osama bin Laden. Al-Qaeda carried out the 9/11 attacks on the USA (11 September 2001).
A US-led invasion (October 2001) removed the Taliban. NATO's ISAF force tried to rebuild the country under Hamid Karzai. British troops fought in Helmand from 2006.

The USA and Britain invaded Iraq in March 2003, claiming Saddam had weapons of mass destruction (none were found). Saddam was captured in December 2003 and executed in 2006.
An insurgency followed, with fighting between groups. British troops based around Basra left Iraq in 2009.

Which country did Iraq invade in August 1990?: Kuwait: The UN demanded Iraq withdraw.
What was Operation Desert Storm (1991)?: The US-led attack to free Kuwait: Britain was part of the coalition.
Who gave shelter to al-Qaeda in Afghanistan?: The Taliban: The Taliban took Kabul in 1996.
What led to the US-led invasion of Afghanistan in October 2001?: The 9/11 attacks: The Taliban refused to hand over bin Laden.
Which Afghan province did British troops fight in from 2006?: Helmand: Many British soldiers were killed there.
What reason was given for invading Iraq in 2003?: Claims that Saddam had weapons of mass destruction: No such weapons were found.
When was Saddam Hussein captured?: December 2003: He was executed in 2006.
When did British troops leave Iraq?: 2009: They had been based around Basra.