The Burly Brawl was an infamous fight between Neo and Smith, now a virus in the Matrix, during the near-end of the Machine War. Neo used the powers of The One to fight off Smith and his army of assimilated copies. At the end of the epic battle, Neo was surrounded by Smiths and fled from the park.
We can never see past the choices we don't understand."”
"Are you saying I have to choose whether Trinity lives or dies?"
"No, you've already made the choice. Now you have to understand it.
― The Oracle and Neo[src]
After passing Seraph's test, Neo was able to use a backdoor to gain access to a playground wherethe Oracle was sitting on a bench waiting for him. During their conversation, the Oracle told Neo about his journey to the Source and to reach there Neo must find the Exile known as the Keymaker, as he is the only one that can lead him to The Source. Before their conversation ended, the Oracle informed Neo that the Keymaker is held captive by the Merovingian and Neo must find the Merovingian and rescue the Keymaker.
We're here because of you Mr. Anderson. We're here to take from you what you tried to take from us; purpose.”
― Smith to Neo[src]
The Oracle wished Neo good luck before leaving the playground with Seraph through the door that they came in from. As soon as they left, Smith from the far end of the playground started walking towards Neo. Neo turns to see Smith walking towards him with the crows flying away. The program then asked if Neo received his package, revealing he was the anonymous visitor at the Crisis Meeting, with Neo confirming it. The Nebuchadnezzar crew, witnessed this from the monitors, with Morpheus being shocked at Smith's apparent return due to his apparently being destroyed by Neo earlier, with Link commenting that regardless of whether it's Smith or not, the individual definitely wasn't reading like an Agent. Smith, after learning that Neo wasn't surprised at his return yet didn't understand why, explained he was now connected to Neo, was no longer an Agent of the Matrix due to being "compelled to disobey" his directive of returning to The Source, and he wasn't sure how any of this came to be. Thanking Neo for "unplugging" him, Smith revealed his opinion that one exists with a purpose. Smith decides that he must use his freedom to gain control of the system to satisfy his "purpose" and his desire. After the Smiths revealed themselves from behind gates, doors, and other objects; each one adding to their monologue on the concept of purpose and their personal goal, to get rid of Neo as a response of how he nearly tried to get rid of Smith's "purpose."
Attacking without warning, Smith tried to assimilate Neo, all while "assuring" Neo that his assimilation will be completed soon. Determined to live, Neo concentrated on the affected area, forcing the infection back towards Smith's hand. Neo then swiftly yanked himself free. Immediately after freeing himself, two of the Smiths beside Neo grabbed onto his shoulders and Neo blocked against them and attacked them as well as another Smith behind him and in front of him. After his swift physical defense, a fight between himself and the eight Smiths present was underway.
Me, me, me..."”
― Smith assimilating Agent Thompson[src]
During the Burly Brawl Neo fought many Smiths simultaneously. More and more Smiths would enter the scene and eventually forcing Neo to flee.
During the fight, a Bluepill enters the playground area and witnessed the battle taking place. However, she was soon possessed by Agent Thompson at the entrance of the playground. Before he neared the Smith clones another Smith appeared next to him and starts assimilating him, also replying to Thompson's recognition of him by confirming it was indeed him, and also mockingly says "me, me, me..." while absorbing the Agent, with the Smith clone then agreeing with Smith. Smith successfullly assimilates the body Thompson possessed but failed to assimilate Thompson himself, since he abandoned the body before the assimilation process was over. The newly assimilated Smith starts walking towards the center of the playground and the fight continues.
Neo realized that many more Smiths were joining the fight. The Smiths started to attack Neo simultaneously. Neo was able to grab hold of a tether-ball pole from the ground as a weapon. After hitting one Smith hard enough that he flew into the bench where The Oracle was once sitting on before, he commented on how more was on the way. Neo continued to battle with all the Smiths until he realized that there were too many to handle. Another Smith attacked him and Neo fell to the ground and the Smiths dogpiled on top of Neo. Buried by all the Smiths, Neo struggled to break free.After forcing all of them to break away from Neo, he realized that he has enough room to escape.
Neo realized he was surrounded by the recurring number of Smiths. He then flew straight up into the sky, leaving the some 195 total copies of Smiths behind. After witnessing Neo fly away, Smith and his clones stared into the sky and returned to Mega City to assimilate more copies to eventually try to rule the Matrix.
Upon reentering the Real World, Neo told the crew of the Nebuchadnezzar that when Smith tried to clone Neo by thrusting his hand into Neo's chest, it felt like he "was back in that hallway. It felt like dying". By this, Neo is speaking of the hallway outside of Room 303 in the Heart O' The City Hotel, where he was shot to death by Smith before being resurrected as The One in the first film.
Neo then told the others about what The Oracle said and their next objective to find The Merovingian and free The Keymaker as he will lead Neo to The Source and they will be closer to ending the Machine War.
This would not be the final encounter Neo had with Smith and his clones, as he, Morpheus, and the Keymaker would later encounter them in the building holding the door to The Source, in fact, in the hallway immediately leading to that door, and proceeded to fight them once more, with only the shutdown of the power station preventing the Smiths from defeating them, albeit at the cost of the Keymaker.