From Revolutionary Russia, 1891-1991: A History, by Orlando Figes (Metropolitan, 2014), Kindle Loc. 1480-1493:
In the big industrial cities there was a similar process of radicalization in the wake of the Kornilov crisis. The Bolsheviks were the principal beneficiaries of this, winning their first majority in the Petrograd Soviet on 31 August. The Soviets of Riga, Saratov and Moscow fell to them soon afterwards. The rising fortunes of the Bolsheviks were due mainly to the fact that they were the only major political party which stood uncompromisingly for ‘All power to the Soviets’.
This point bears emphasizing, for one of the most basic misconceptions about the October Revolution is that the Bolsheviks were swept to power on a tide of mass support for the Party. They were not. The October insurrection was a coup d’état, actively supported by a small minority of the population, but it took place in the midst of a social revolution, which was focused on the popular ideal of Soviet power. After the Kornilov crisis there was a sudden outpouring of resolutions from factories, villages and army units calling for a Soviet government. But almost without exception they called on all the socialist parties to participate in its establishment, and often showed a marked impatience with their factional disputes.
The real significance of the Kornilov Affair was that it reinforced the popular belief in a ‘counter-revolutionary’ threat against the Soviet—a threat the Bolsheviks would invoke to mobilize the Red Guards and other militants in October. In this sense the Kornilov Affair was a dress rehearsal for the Bolshevik seizure of power. The Bolshevik Military Organization emerged from the underground—where it had been since July—with renewed strength from its participation in the struggle against Kornilov. The Red Guards were also reinforced: 40,000 of them had been armed in the crisis. As Trotsky later wrote, ‘the army that rose against Kornilov was the army-to-be of the October revolution’.