The word pröjsa is a colloquial way of saying 'to pay', as in exchanging money for products or services. In standard Swedish, the word for 'pay' is betala, which comes from an older word meaning 'to count/calculate'.
The Swedish language also has the noun pröjs, which means 'payment' and is equivalent to betalning.
Pröjsa has been recorded in Swedish since the early 1900s, and it comes from the Romani language, one of Sweden's official minority languages. Roma have lived in Sweden since at least the 16th century, and their language has influenced Swedish, with other loan words such as tjej. Pröjsa comes from the Romani word prejsa, which means the same thing.
Pröjsa can be used simply as an alternative to betala, but it sometimes has the connotation of paying an unexpected cost or an unexpectedly high one, in which case you could translate it as 'pay up' or 'cough up'.
Slutligen är det konsumenten som får pröjsa
In the end, it's the consumer who pays the price
Det är personalen som måste pröjsa springnotan
It's the staff who have to cough up for the bill if customers leave without paying (note: springnota comes from springa meaning to 'run' and nota meaning 'bill')