It's switching your residence permit from one type to another without leaving Italy. Common conversions include going from a study permit to a work permit after graduation, or from a seasonal work permit to a regular one.
Without conversion you'd have to leave, get a new visa from abroad, and start over. With it, you keep your time-in-Italy clock running, which matters for things like the long-term EU permit and eventually citizenship.
"Wei finished her master's in Pavia and got a job offer from a Milan tech company before her student permit expired. Her lawyer filed for conversion to a work permit using a slot reserved for graduates in the Decreto Flussi."
Not every conversion is unlimited. Going from study to work usually requires a slot inside the yearly quota, so check timing before you celebrate the job offer.
Official source
Ministero dell'Interno
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