The title of course refers to the particular time in which this ironic story takes place, as it occurs at "thirty minutes past six on an early March evening" with dusk having fallen "heavily" over the scene. Of course, the importance of the title is not just physical, as it also corresponds to the mood of its protagonist, who attaches a special significance to this particular time:
The scene pleased Gortsby and harmonised with his present mood. Dusk, to his mind, was the hour of the defeated. Men and women, who had fought and lost, who hid their fallen fortunes and dead hopes as far as possible from the scrutiny of the curioius, came forth in this hour of gloaming, when their shabby clothes and bowed shoulders and unhappy eyes might pass unnoticed, or, at any rate, unrecognised.
Note the way that dusk is attached to human failure and discontent. Dusk then seems to be, in the narrator's mind, a time when humans can walk around in the encroching darkness and not have to hide their failures. There is an intense irony in this, as Gortsby feels he is able to judge by circumstances as he looks at others and imagines their situations, yet clearly he makes a massive mistake when he finds the bar of soap and mistakenly believes the young man, giving him money, when the young man had been trying to deceive him all along. Dusk seems to have only masked Gortsby's own abilities to discern the truth.