There's a different version of the hadith which appears in the sunan books which partly explains the meaning:
"The Messenger of Allah said: 'Whoever has a speck of pride (arrogance) in his heart, shall not be admitted into Paradise. And whoever has a speck of faith in his heart, shall not be admitted in to the Fire.'" He said: "So a man said to him: 'I like for my clothes to be nice, and my sandals to be nice?' So he said: 'Indeed Allah loves beauty. But pride is refusing the truth and belittling the people.'" (Jami' at-Tirmidhi https://sunnah.com/tirmidhi/27/105, Sunan abi Dawod https://sunnah.com/abudawud/34/72, Sunan ibn Majah https://sunnah.com/urn/1343120)
Note that in this translation arrogance stands for كبرياء or كبر (which was translated in the version of imam Muslim as pride). To clarify the term: كبرياء or كبر in Arabic commes from the verb كبر which means become great, it refers to having the impression to be better/greater than others and acting like that ...
Imam at-Tirmidhi commented the hadith above by the addition (which was not translated on sunnah.com) saying: "None shall enter the Fire (of Hell) who has in his heart the weight of a mustard seed of Iman" means he will not stay there forever, and he added as a proof the hadith of abu Said al-Khudri (https://sunnah.com/urn/727970).
So the overall meaning of this hadith is that none will enter Hellfire or Paradise until they have got justice for their good (recompense) and bad deeds (punishment). And that it is wrong to think that it is impossible for a person that has arrogance in his heart to enter Hellfire no matter how great his faith is.
Note there are further ahadith that remain us about the limitation on pride/arrogance:
Three (are the persons) with whom Allah would neither speak, nor would He absolve them on the Day of Resurrection. Abu Mu'awiya added: He would not look at them and there is grievous torment for them: the aged adulterer, the liar king and the proud destitute. (Sahih Muslim https://sunnah.com/muslim/1/202)
Even a poor person can be punished for being arrogant. (here again كبر was translated by pride/proud).
Allah, the Exalted and Glorious, said: Glory is His lower garment and Majesty is His cloak and (Allah says, ) He who contends with Me in regard to them I shall torment him. (Sahih Muslim https://sunnah.com/muslim/45/177)
In this hadith كبرياء was translated by the word Majesty. It is an attribute of Allah so none of His creation should act like he has the same attribute!
See also this fatwa (https://islamqa.info/en/answers/170526/commentary-on-the-hadeeth-no-one-who-has-an-atoms-weight-of-faith-in-his-heart-will-enter-hell) on the meaning of the hadith.
