The police of Gotham City use the Bat-Signal to summon Batman when criminals act a fool. All the cops have to do is go on top of their building and fire up this modified searchlight and Batman swoops down from on high. Ass-kickery ensues.
The origin of the Bat-Signal is inconsistent. When Michael Keaton wore the Bat-Gear and stomped on The Joker's henchpersons in 1989's Batman movie, the Bat-Signal was given to the police by Batman. However, 2005's Batman Begins presented a different, well, beginning to the Bat-Story. Then detective James Gordon fashions his own Bat-Signal that resembles the image projected earlier in the movie when Batman, played by Christian Bale, chained evildoer Falcone to a searchlight. I don't remember how it came about for the TV show back in the day. Nor do I read the comics, so feel free to clue me in.
Paging Mr. Batman
Speaking of back in the day, it's funny to see that Bat-based communications have regressed as the series wore on. Adam West frequently got hot tips from the Mayor on the Bat-Phone. However, no such voice communications exists for more recent Batpersons. Not even a Bat-Pager. It seems like there should be some kind of backup system in place. What happens when there are no clouds in Gotham City? Then there is no reflective surface in the sky to bounce the signal off of. Kinda sucks if Two Face decided to steal your company's latest doomsday device and Batman is kicked back on the Bat-Chair eating Ramen because of the clear sky.
Incoming call from...
For trivia's sake, it can be noted that it isn't always the police who broadcast the Bat-Signal. When Nicole Kidman's character Chase Meridian wanted to hump Val Kilmer's Bat-Leg in Batman Forever, she used the Bat-Signal to lure him to police headquarters. Later in the movie, The Riddler and Two Face, played by Jim Carrey and Tommy Lee Jones respectively, project an altered Bat-Signal to call out Batman for the final showdown.
Check back later--same Bat-Time, same Bat-Channel!