The cinder path runs "before the new red houses...bright brick houses with shining roofs", while the concrete pavement lies before the drab "little brown houses" where Eveline lives. I believe the contrast is meant to accentuate the difference between the old and stagnant, and the new and vibrant elements in Eveline's world.
The concrete path is functional; it is not meant to be pretty. It might be representative of Eveline's life until now - comfortable but duty-bound. Eveline's existence is rooted in the past and in things that are old; it lacks excitement and the potential for renewal and discovery.
The cinder path has an aspect of rustic quaintness. It has personality, and, along with the brick houses which have only recently been built by a man from Belfast, an aesthetic appeal. The cinder path represents progress and freshness, a step away from the plain brown houses into a changing future. Eveline can see a world of beauty and promise from her window, but when her opportunity comes, she does not have the strength to step out and become a part of it.