It has, like most ritual with material sacrifies, not really a connection to the Buddha-Dhamma, aside of the possible devotion and sacrify, metta and compassion, to ones ancestors, deities or spirits, which are possible wholesome deeds and generally praised by the Buddha (sacrifies for deities and ancestors)
It's a very usual ritual, mostly performed by people with Chinese or Vietnamese ancestors all over SEAsia on Chinese fest days and has it's origin in certain Asian ancestor-cults and religions.
Earlier real money was used which of course is mostly not legal, so copies and fake prints are usually used to be burned in front of the houses.
As a one of a childs "duty" torward death relatives:
from the Sigalovada Sutta: The Discourse to Sigala - The Layperson's Code of Discipline
"In five ways, young householder, a child should minister to his parents as the East:
(i) Having supported me I shall support them,
(ii) I shall do their duties,
(iii) I shall keep the family tradition,
(iv) I shall make myself worthy of my inheritance,
(v) furthermore I shall offer alms in honor of my departed relatives.
Note by the translator: 9. This is a sacred custom of the Aryans who never forgot the dead. This tradition is still faithfully observed by the Buddhists of Sri Lanka who make ceremonial offerings of alms to the monks on the eighth day, in the third month, and on each anniversary of the demise of the parents. Merit of these good actions is offered to the departed after such ceremony. Moreover after every punna-kamma (good action), a Buddhist never fails to think of his parents and offer merit. Such is the loyalty and the gratitude shown to parents as advised by the Buddha.
from: Tirokudda Kanda: Hungry Shades Outside the Walls
...Offerings should be given for the dead
when one reflects thus
on things done in the past.
For no weeping,
no other lamentation
benefits the dead
whose relatives persist in that way.
But when this offering is given, well-placed in the Sangha,
it works for their long-term benefit
and they profit immediately.
In this way
the proper duty to relatives has been shown,
great honor has been done to the dead,
and monks have been given strength:
The merit you've acquire
[Note: This is a gift of Dhamma and not meant for commercial purpose or other wordily gains]