If you are carrying an accursed or infernal urn, the urn will be charged in place of receiving the drop. Accursed urns can store up to 25 dropped accursed ashes and yield 375 prayer experience when teleported. Infernal urns will be full after 125 accursed ashes and give 1875 prayer experience. That equals to 15 prayer experience for each set of accursed ashes, the same amount as big bones. Carrying urns with you while training on lesser or greater demons could be useful to get additional prayer experience. However, as lesser demons, the lowest levelled monster that drop accursed ashes in F2P, are far stronger than Hill giants, most commonly killed for their drop of big bones, this way of training is not recommended. If you buy the bones or ashes to train, the latter would be slightly cheaper, but slower.
Prior to the release of impious and accursed ashes, F2P players could only train Prayer by burying bones.
This table can be used to compare and decide on how to train with the ashes for the most desired cost versus experience gained. Notice how the cost in coins per XP point varies greatly depending on how the ashes are used — but also remember that the different methods have different training speeds.