Start here: https://en.wikipedia.org/wiki/15_February_2003_anti-war_protests

Specific news articles about that day:

https://web.archive.org/web/20040904214302/http://www.guinnessworldrecords.com/content_pages/record.asp?recordid=54365

From Guinness World Records:

On February 15, 2003, anti-war rallies took place across the globe – the largest occurring in Rome, Italy, where a crowd of 3 million gathered to protest against the USA’s threat to invade Iraq. Police figures report that millions more demonstrated in nearly 600 cities worldwide: on the same day, 1.3 million rallied in Barcelona, Spain, 1 million participated in a peace march through the streets of London, UK, and 500,00 people in Melbourne and Sydney, Australia, joined the biggest marches since the Vietnam War peace protests.

https://web.archive.org/web/20100326221254/http://www.socialistworker.co.uk/art.php?id=6067

The French political scientist Dominique Reynié has estimated that, between 3 January and 12 April 2003, some 36 million people took part in nearly 3,000 protests around the world against the Iraq war.

(It’s worth noting here that I have been unable to find Dominique Reynié’s paper that estimates this. I have searched and searched for a PDF with no luck. Lots of references to this work, but can’t seem to find the actual document.)

https://web.archive.org/web/20190921125652/http://news.bbc.co.uk/2/hi/europe/2765215.stm

Between six and 10 million people are thought to have marched in up to 60 countries over the weekend - the largest demonstrations of their kind since the Vietnam War.

A key aspect of what made it so big was because it was happening worldwide, simultaneously, in multiple cities all over the world.