Understand it's a reference to Job from the Bible, who was known for enduring suffering with perseverance. She had the patience of Job when she calmly waited for hours at the airport.
Pro Tip 2/3
Not Literal
It's an exaggeration; nobody can have infinite patience, but some situations demand a lot. Managing to assemble that complex furniture surely required the patience of Job.
Pro Tip 3/3
Positive Praise
Using this phrase is a positive way to praise someone's extraordinary ability to wait or tolerate. The nurse's care for her patient showed she really had the patience of Job.