Written by Amber:

The pirates came to loathe the goddess Calypso for her unpredictability and her temperamental mood, a direct influence on the sea they sailed on. Her tantrums forced them to work harder if they wanted to survive and live their way of life, so when Davy Jones approached the nine pirate lords with the intention of binding Calypso in human form, they agreed wholeheartedly in the hopes that the sea would become less treacherous in turn.

Davy Jones
Davy Jones was betraying his lover the very moment he asked for her to be bound in her bones. It was revenge for when she stood him up after he awaited the one moment they could be together after ten years: the one moment he could stand on land. Calypso had given him the duty of ferrying souls lost at sea to the afterlife, rendering him incapable of stepping foot on land until a decade passed since he was given the position. They could not be together at that time, and once she left him standing alone he lost all trust in her. Grudging feelings towards her remained throughout the entire series, even though it is clear he always loved her.

Release
The process for binding Calypso isn't known, though it involves nine pieces of eight (or rather as Gibbs described them, "whatever we happened to have in our pockets at the time.") that each pirate lord provides. The same talismans are required to release her, and must be burned while speaking "Calypso, I release you from your human bonds" as if to a lover. The first Brethren Court bound her in order to tame the sea, while the fourth freed her in the hopes that she might aid them in the fight against Beckett. Once she learned of Davy Jones' betrayal, she decided not to help either side, instead providing a strong wind for a fair fight by striking the sea with lightning in order to create a whirlpool of doom.