From  scuola meaning "school".

The authors agree that the surname derives from the late Latin word schola, with the meaning of "school." E. Rossoni notes that it probably alluded to belonging to a group of disciples of a master craftsman. V. Blunda, on the other hand, analyzes it from a Sicilian and dialect perspective: the word scòla goes back to the Latin schola, a loanword from the Greek scholē, consolidated in urban toponymy, and as a surname it could have originated in a microtoponym applied to one who resided next to a school building or was engaged in teaching.

Rossoni indicates that Scola, a fairly rare surname, is distributed throughout Italy, while the related surname Scolari is specific to Lombardy and the Verona area. He adds that Scolari is documented from the medieval period: Dino Compagni cites a Scolari de' Lamberti family in his chronicle, and in 1411 the emperor Sigismund sent to Friuli troops under the command of the Florentine Pippo Scolari.