A death occurs when the player's HP (hitpoints/hearts) hits 0. On respawn, the player is sent to Lumbridge and the following occurs.
When a player dies, they are provided with a menu screen which allows them to pick 3 items they would like to keep. These items are then kept, while the remainder are dropped at the location of death. If the remaining items are not picked up within 5 minutes, they despawn and can never be retrieved. During this time, other players are free to pick up and keep such items for themselves.
After the player decides to respawn, they are shown a screen similar to a chest. Within this menu is a list of all the items dropped. The player is allowed to choose a total of 3 items to keep instantly, then must run back to their location of death to collect the rest.