The retarded Green function G^R(t,t') = −iθ(t−t') e^(−iω₀(t−t')) e^(−γ(t−t')/2) is the causal response of an oscillator to a delta-function impulse at t=t'. "Retarded" means G^R = 0 for t < t' — the system responds only after the source, enforcing causality. The general solution is then a convolution: x(t) = ∫G^R(t,t') f(t') dt'. In frequency space, G^R(ω) = 1/(ω²₀ − ω² − iγω), with poles below the real axis — this is the signature of retardation and the origin of the Kramers-Kronig relations. Advanced Green functions have poles above the real axis and describe acausal, "time-reversed" solutions.