The Deplorable Word was a spell from the now dead world of Charn. It was a magical word, which, if spoken with the proper ceremonies, would destroy all life in the world, except for the person who spoke it.
The existence of the Deplorable Word was a closely guarded secret, which was passed down through generations of the magically adept ruling family of Charn, who had bound themselves with oaths never even to seek knowledge of it. Jadis, though, more power-hungry than her ancestors, including her more recent ones, "searched long for it, and paid a terrible price to learn it".
The war with her sister, an extremely bloody world war, was apparently just a power struggle between the two, which the sister won. Jadis waited to use the word until she met with her victorious sister at the steps to her palace, offering her the chance to surrender if she acknowledged her as Charn's one true ruler. Her sister, however, refused, and so Jadis spoke the Deplorable Word, and a moment later she was the only living thing left under her world's red sun.
Afterward, Jadis showed no remorse, and even narcissically blamed her sister for her act; "Her greed has destroyed the whole world!" Besides killing Aslan on the Stone Table, this was Jadis's most evil known act.
While it is not ultimately known why Jadis didn't use the Deplorable Word to destroy Narnia when she was defeated at the Battle of Beruna, before she was killed by Aslan, there is evidence that the spell, along with numerous other magical powers she once possessed, may have only worked in the world of Charn: -
Alternatively, if the spell had worked, she may not have had time to use it before she was killed by Aslan, since his attack was a surprise, and the use of the word required certain ceremonies. Or it may be that Aslan had already taken other unknown actions to prevent her from using it.
The Deplorable Word should not be confused with a lesser spell, also involving a magic word, which Jadis used to destroy the gates of the palace of Charn.
Aslan warned Digory and Polly that in our own world, a secret alike to that of the Deplorable Word might soon be revealed. Given that this all took place around the year 1900, he may possibly have been referring to the atomic bomb.