While, wile, beguile, fleet mean to pass time, especially leisure time, without being bored.
One whiles or wiles away a space of time by causing it to be filled by something pleasant, diverting, or amusing.
One beguiles a space of leisure time or its tedium or irksomeness by occupying that time with some agreeable and not necessarily time-wasting employment.
One fleets the time by causing it to pass quickly or imperceptibly; the term may or may not imply an effort to while time away.