Piazza della Signoria has been the political heart of the city from the Middle Ages to the present day. It is a singular urbanistic creation that began taking shape from 1268 onwards, when the Guelph party gained control of the city again and decided to raze the houses of their Ghibelline rivals to the ground.
The first to be destroyed were the towers belonging to the Foraboschi and the Uberti families, in spite of the fact that the head of the family (the famous Farinata celebrated by Dante in his "Comedy"), had defended the city from destruction after its army had been disastrously defeated at the battle of Montaperti (September 4th 1260) by the Ghibelline coalition led by Siena.
In the end 36 houses were demolished which explains the unusual "L" shape of the square and why the buildings around it are unaligned, all that remained after the city's enemies had all been "wiped out" (nothing was ever to be built on the site again).
Its gets its name of course from the most important monument there, Palazzo della Signoria, designed by Arnolfo di Cambio in 1298-99 (much of it already completed by 1302, only three years later) for the seat of the Republican government and which was later to host the Gonfalonier of Justice and the Priors of the Arts (it was in fact at first called Palazzo dei Priori).