Brad Dellebuur, city transportation planner, says pushing the button sends a signal to the intersection's traffic controller that a pedestrian is present and enters the "walk" signal into the system's cycle.
"If you don't press it, some intersections won't give a walk signal," Dellebuur says. The traffic light timing is also determined by the amount of vehicular traffic, which is picked up by sensors imbedded in the road.
In other words, pushing the button won't make the light change right away, or within a certain time from when the button is activated. You'll still have to wait, but a shorter period as the traffic light interval is shortened.
If you don't push the light, the pedestrian walk signal still comes on, but, for instance, after 60 seconds instead of 40.

It's not just distrust that makes people push a crosswalk button that has probably been pushed already. It's also ritual, says Jim Gibson, social psychologist at UVic, and very much like pushing an elevator button that is already illuminated.
"It's part of crossing the intersection," Gibson says. "We want to cross, and pushing the button first is part of that ritual.
"We go on automatic pilot because ritual behaviour saves our brains from having to think about activities that are very routine."