It’s a superpower, a product of her metagene. Her other primary ability is that she’s a martial artist, roughly a second tier DC hand to hand combatant (the first tier being Batman, Batgirl, Lady Shiva, Richard Dragon, poissibly Cheshire, maybe one or two others). She was initially trained by her “uncle” Wildcat (Ted Grant), because her mother didn’t want her to get into the biz and refused to train her, but has since trained in and mastered several others; she officially knows seven forms of martial arts. Recently, Lady Shiva invited her to train as an apprentice, but being an apprentice to an assassin isn’t the most heroic thing in the world.
I thought that she had lost the sonic scream some time back when she was captured and badly beaten by drug dealers while working undercover, with her vocal cords being permanently damaged (Longbow Hunters 2), but krodil’s post seems to contradict that. Invasion happened after Longbow, so I’ll assume his info is more up to date than mine.
More recently, Rha’s Al Ghul decided he wanted her to be his mate. He had prepared a Lazarus pit to brainwash her, but an attack by Powergirl, Blue Beetle and others interrupted the plans and she was beaten nearly to death by a henchman while Rha’s escaped. Dinah wanted Barbara to use the pit to heal her paralysis, but Barbara had Beetle put Canary into the pit, which healed her completely, inlcuding her canary cry. (Birds of Prey 34-35).
She can control it. It can be a really loud sound broadcast in all directions, loud enough to kill ordinary people exposed for long enough, or enough to disrupt opponent’s balance and thought processes. She can focus it into a tight beam, as a concussive force against single opponents.
In classic stories, she’d usually use her scream and martial arts (in the earliest stories, Judo) in conjunction, throwing her opponents off balance with the cry, then kicking their butts hand to hand.
It seems to take some concentration and energy, as I don’t recall seeing her use it simultaneously with hand to hand, though it’s not inconcievable that she would do so.