How old is it?
If you had it for a long time that might be a reason.
Have you dropped it at all or shook it a lot?
I dropped my iPhone a couple times and it did not turn on until the day after that.
Also when I was younger I shook my mothers iPad a couple of times and it didn't turn on either until
the next day.
Have you charged it or changed the battery?
That is another possible reason especially if you used it while it was charging.
What I'm saying is that you can either run down or kill the battery like that.
Also the more you use your phone while its charging the faster it will run out of battery's.
The last reason i can think of so far is magnets.
I know what your thinking,how can magnets have anything to do with your phone not turning on.
Magnets can screw up the circuit board and the compass on your iPhone so it won't turn on or turn on correctly and if it does turn on you will probably have problems getting to your phone home sceen