He found, as he often told my sister, broken horse-shoes (a "bad sign"), met cross-eyed women, another "bad sign," was pursued apparently by the inimical number thirteen—and all these little straws depressed him horribly.
AND
One day on coming back home he found one of his hats lying on his bed, accidentally put there by one of the children, and according to my sister, who was present at the time, he was all but petrified by the sight of it. To him it was the death-sign.
These sentences characterize Paul as a superstitious person. A superstitious person is one who believes in things that are irrational. Some common superstitions are: a broken mirror equals 7 years of bad luck, or a black cat crossing one's path signals bad things are coming. In these sentences Paul believes things like broken-horse shoes, cross-eyed women, the number thirteen, and his hat lying on his bed all signal bad things are going to happen.