This verse describes a violent and emotional outburst from a crowd in Jerusalem who were listening to Paul the Apostle defend himself after being arrested. Let's break down the meaning of each element:

"As they cried out": This indicates that the crowd reacted with a loud, passionate, and likely angry vocalization. They were not merely disagreeing; they were expressing intense opposition and outrage.
"and threw off their cloaks": This action had a few possible interpretations:
Disrespect: Removing their cloaks could have been a sign of disrespect and rejection towards Paul and his message.
Preparation for violence: Casting aside cloaks would make it easier to move freely, suggesting they were preparing for a physical confrontation or riot.
Emotional outburst: In moments of extreme emotion, people sometimes discard items of clothing without a specific rational reason.
"and threw dust into the air": This was a traditional Semitic expression of extreme grief, anger, or indignation. It conveyed:
Grief and mourning: Throwing dust over oneself was a traditional sign of mourning and lament.
Indignation and outrage: It could also express moral outrage and judgment against someone, almost like a curse or a rejection of the person and their words.
Despair: It might reflect a sense of hopelessness or despair in the face of what they perceived as blasphemy or heresy.

Overall Meaning

The verse illustrates that the crowd became utterly incensed by Paul's defense. They were likely angered by his mention of preaching to Gentiles and the idea that God's salvation was also for them. Their actions were a sign of deep-seated religious and cultural prejudice. The outburst created a chaotic and threatening situation that ultimately led to Paul's re-arrest and further legal troubles. The verse highlights the intense hostility and opposition Paul faced as he preached the Gospel.