Get the perfect balance
Getting tyre pressure right is vital at the top level and greatly increases enjoyment for all cyclists. On rough surfaces, a tyre at lower pressure can absorb more of the bumps than a tyre at higher pressure, with less deflection of the bike and its rider. Rolling on a perfectly smooth surface, a tyre at high pressure has less rolling resistance and therefore rolls faster than the same tyre would when run at lower pressure, for a given power input.
However, on rough, irregular surface tyres at lower pressure roll faster because they can deform to the surface, absorbing bumps without transferring forces to the rider or sapping the momentum of the bike and rider. At lower pressure, the contact patch between the tyre and the ground is larger. This increases grip and improves cornering traction.