The basic idea behind the propagator model is that order flow can be treated as a propagating wave that spreads through the market and affects prices. Thus given that we usually execute multiple orders for a given "meta" (big) trade, managing the effects of those earlier orders on later orders can have non-negligible impact on the execution performance. The propagator model then gives some solution to get the optimized execution under those assumptions. You can refer to https://www.goodreads.com/book/show/39096959-trades-quotes-a... for more information