Paul VI established the Synod of Bishops by the motu proprio Apostolica Sollicitudo on 15 September 1965, while the Second Vatican Council was still sitting. The timing is the explanation. The Council had gathered the world's bishops in Rome for four sessions and had put a great deal of weight on collegiality, the idea that the bishops together with the pope share responsibility for the whole church; and the Council was about to end. The Synod was the mechanism by which something of that gathering would continue without keeping two and a half thousand bishops permanently in Rome.
Its assemblies come in three kinds. Ordinary general assemblies meet at intervals of a few years on a topic chosen by the pope, with most members elected by the episcopal conferences of the world. Extraordinary assemblies are smaller and quicker, for matters needing prompt attention. Special assemblies cover a region, and those on Africa, on Lebanon, on the Middle East and on the Amazon have each addressed a set of questions that a global assembly would have handled thinly.
The working method is stable: a preparatory outline, a consultation, a working document, then the assembly itself, and afterwards a post-synodal apostolic exhortation issued by the pope, which is the document that actually carries teaching weight.