The statement means exactly what it says ... pedestrian push buttons serve a specific purpose, and are essential in certain circumstances.

In locations where numbers of pedestrians are not high, the timing of the traffic signals is usually optimized for the vehicular movements, with a separate set of parameters established for those signal cycles when a pedestrian needs to cross. Pushing the button sends a "call" to the signal controller which then ensures that the pedestrian "walk" symbol is displayed at the next available opportunity. It may (or may not, depending on how it is programmed) shorten the green time for other signal phases in order to get the "walk" symbol displayed sooner, but rarely are things set such that pushing the button immediately gives the pedestrian complete priority. The lack of an instantaneous display of the pedestrian "walk" is what frustrates people and makes them think that the button is useless ... though buttons do fail and need replacement sometimes. The common practice of standing there banging the button continuously really serves no purpose other than "venting" I suppose. Even worse is hitting every pedestrian button at a signal that has buttons for different directions of pedestrian movement ... that could end up with there being more delay in you getting the "walk" symbol you are waiting for.

I will clue you in on the traffic signal button. No, the button is not a placebo. That said, what most people don’t understand, is that pushing it more than once is totally useless. The first person to push the button, within the current light sequence, trips a solenoid that lets the controller know someone is waiting. Once that solenoid is tripped it does absolutely no good to push the button additional times. The controller does not count the number of people waiting. It is strictly a yes/no parameter.