In Japanese, saisen (賽銭) is money offered to the gods or bodhisattvas.
This design allows coins to be tossed in, while still preventing the money from being retrieved easily.
Some have grates made of round bars, or have borders that slope downward, allowing the money to slide into the box easily.
[1] Five yen coins are a popular offering at saisen boxes due to the pun between five yen, go-en (五円), and the concept of an unseen connection between humans who know each other, go-en (御縁).
Some shrine priests have caught thieves in the act, while others take preventive measures by adding covers to the saisen boxes.