A Dismissal is the means by which a magician releases a demon from its earthly obligations and sends it back to the Other Place.
As with other forms of magic, a Dismissal requires a specific procedure and words and will not work correctly, or may even backfire, if done incorrectly. A Dismissal requires a pentacle, which has certain lines and Heiroglyphs to cancel out other commands and bindings, such as Adelbrand's pentacle requires a certain circle to cancel it.
As presence on Earth wears away a demon's essence, they will generally work hard and without outward complaint in the hope of securing a dismissal, though there are exceptions. Bartimaeus, with his control over his master's birth-name was able to continuously pester Nathaniel, in hopes of receiving a dismissal.
Other spirits, such as the foliot Simpkin, were able to nearly completely cut-off their ties to the Other Place, instead remaining on Earth for continuous periods without a Dismissal, ignoring the pain in their form from continued service.
However, the consequences of being indefinitely trapped on earth are best seen in Honorius, an Afrit, who was charged to forever protect his master's corpse. He went completely insane because of his disattachment from the Other Place, even though he felt no pain within the rotten corpse.
A demon that was not Dismissed, could in most cases, still be released from their Earthly ties if the magician who had summoned them was killed. Honorius was an unusual example of this not being the case, having been bound to Gladstone's bones by a powerful spell that took effect after the magician's death.
While a spirit could normally only be dismissed by its master, Uraziel, the Greater spirit of the Ring of Solomon, had the possibly unique capability to dismiss summoned spirits within its presence in an instant.