Why do Catholic laity cross themselves three times before the Gospel is read? Why does the laity (and sometimes the priest) cross themselves 3 time before the Gospel is read? 

Like holding hands during the Lord's Prayer, and unlike bowing at the mention of the Incarnation during the Creed, it's not something that is called out in any of the missals or Mass cards I've ever seen in the pews, but it seems to be a pretty common practice; at least in my diocese.
Before the Gospel is read, a Catholic makes signs of the cross, with the thumb, on his or her


forehead,
mouth, and
heart,


which represents that the Catholic must


understand the Gospel,
proclaim it, and
"take it to heart," i.e., put it into practice, with charity.


Dom Prosper Guéranger's Explanation of the Prayers and Ceremonies of the Holy Mass (hardcover ed. p. 32-33) says:


  [While the priest] makes the sign of the Cross upon the Book, and at the place where begins the text of the Gospel…[, the priest and the faithful] at the same time, signs himself on the forehead, the lips, and the breast, asking, in virtue of the Cross, which is the source of all grace, that he may always have the Gospel in his heart, and on his lips, and that he may never be ashamed of it.


(I've edited what Dom Guéranger said to apply also to the faithful, not just the deacon. Dom Guéranger is describing a Solemn High Mass, where a priest, deacon who sings the Gospel, and sub-deacon, along with altar servers, assist. The deacon in such Masses does the three signs of the cross to himself just as the faithful do to themselves in all types of Masses, High or Low, before the Gospel. The reason for the three signs of the cross is the same.)