I aam refinancing my house to buoya new house closer to my husbands work. I am planning on renting my existing house but in my refi paperwork it sys that I musy keep the exisitng house as my primary residence for 60 days. What does that mean?

It means that the refinance that you are applying for on your current home is a loan for a owner occupant. If you are refinancing to pull cash out of buy another home, then it will not be owner occupied and you should advise your loan officer.

Did you mean to say that the new lender on the new home is requiring that you occupy the new residence with in 60 Days?

If you are looking at your refi paperwork, I'm surprised it only says 60 days, I think 1 year is more typical.  If you do not disclose your intention to turn the existing home into a rental you are committing mortgage fraud.  Google FBI + Mortgage Fraud to see what lies ahead for you!  If you have already signed, I would recommend rescinding the transaction.