Good question! +1 day means that your flight arrives at your destination the day after you departed. However that does not mean that your flight will take a whole full day, only that the next day has begun when your flight is scheduled to land.
A San Francisco to Iceland flight route is marked +1 day on the 15th of December 2016
The flight departs from SFO at 12:50 pm and arrives in KEF at 4:10 am local time.
Actual flight time is only 8:20 hrs, and obviously you‘ll land in Iceland at 9:10 pm on the 15th of December, San Francisco time (PDT). However, due to time difference between San Francisco and Iceland, the clock in Iceland when you land will be 4:10 am (GMT) on the 16th of Dec, the day after.
This is a universal rule in the flight industry and the reason why flights are sometimes marked +1 day.