A first-order analysis assumes a building stays put while loads are applied. Once it actually sways sideways, its own gravity load starts working against it.
A first-order (linear) structural analysis calculates forces and deflections assuming the structure's geometry stays at its original, undeformed position the entire time loads are applied — a simplifying assumption that's accurate enough for many stiff, low-rise structures. But real buildings under wind or seismic load actually move: they sway sideways by some displacement, commonly called Δ. Once that sideways displacement exists, the building's own gravity load, P, is no longer acting through the original centerline — it's acting through the displaced position. That mismatch between where a first-order analysis assumes the load acts and where it actually acts is exactly what P-Delta (second-order) analysis accounts for.