The concert with the biggest amount of people attending was Rod Stewart performing on New Year’s Eve (31 December 1993). There were approximately 3 500 000 people. Now that’s a lot. There is a catch, though. The concert was free, so the estimation is really approximate and it’s kinda cheating a little.
If we take only ticketed concerts with solo performers (ie, excluding musical festivals and such), then the record belongs to the guy whose name you may have never heard of. It’s Vasco Rossi, Italian singer, who gathered 220 000 people on 1 July, 2017 in Italian city called Modena. Before him for 27 years this record was held by Paul McCartney, of whom you may have heard a little more.