Wat is Affine term-structure model?

A short-rate model is an affine term-structure model if its bond prices are exponential-affine in the state: $P(t,T) = \exp\bigl(\mathcal A(t,T)-\mathcal B(t,T)\,x_t\bigr)$ for a state $x_t$ (the short rate or a vector of factors) and deterministic functions $\mathcal A, \mathcal B$. By the Feynman–Kac formula (One Quant Book 4, chapter 4) this holds whenever the drift and the variance of the state are affine in it.