When a bank has too much money (say, from people putting money in a savings account without an equivalent mortgagee to lend the money to), the bank is paying interest to the person with the money in the savings account but isn't recouping this cost from someone paying a mortgage. Or if a bank has signed too many mortgages, they may not have enough money to fulfil them.

To help offset this, banks can lend money from the Reserve Bank (RBNZ) to cover any shortfall that day, or deposit money with them (rates are OCR +/- and amount depending on if it's depositing or lending).

Swap rates are banks lending money to each other to cover differences. But in general, these contracts are longer term (think of the OCR as being like a floating rate, and swap rates being like fixed term rates).

Rising swap rates could mean that the overseas banks that banks here are borrowing from are facing increased costs. Banks here are probably weighing up the risk of using OCR floating rate vs a higher swap rate from borrowing overseas cash.

I guess an explanation here is that globally there may be more demand for these swap contracts as more people are getting new mortgages again, so maybe this pushes up the cost of signing these new swap contracts and therefore pushes up the lending cost?