In its simplest terms, imagine you were just using the yield curve as your single predictor of recessions. Suppose (horribly simplistically) that curve inversions tend to signal downturns in 12-18 months time. The curve 12-18 months ago is thus a relevant variable for whether the economy is going into recession or not today.
It might also be the case that the curve today tends to have started to steepen back up at the point at which the economy starts to shrink. So it might even be the case that the current value of the curve would not then itself be relevant.
These kind of effects are classically represented in traditional econometrics as the "partial adjustment model", or as the "adaptive expectations model". The two are grounded in different, almost completely opposed, theoretical/philosophical assumptions. The former assume (and try to distinguish between) the longer-term versus shorter-term effect of your regressors on your response variable. The latter assume that your regressors already embed some (unknown) anticipation about the future of your response, and so the behaviour of your response also has to reflect revisions to these expectations, when the actual outcomes in your regressors play out differently to the (unknown) expected ones.
As such, the two models appear very different at first. However, there is a big irony here. You end up with the same final structure modelling either via regression, namely:
Y = a.X + b.laggedX + e
hope this helps, DEM