The Heraldic Epochs were the time period before the Era of Solitude, when the Heralds and Knights Radiant battled the Voidbringers in one-hundred Desolations. This era came to an end when Aharietiam, the Last Desolation, was finished and the Heralds abandoned the Oathpact.
Humanity had very little technology during most of the Heraldic Epochs, they did not even know how to forge steel. If they had not been granted Shardblades by the Nahel bond with spren, they would have had to fight the Voidbringers with simple weapons, such as clubs.
The Vorin religion is based on the lie that at the end of the Heraldic Epochs, the Heralds had pushed the Voidbringers back to the Tranquiline Halls and were fighting to force them out of there as well.