Their is a lengthy warning explaining this.

Saving at an Owl will only save the game temporarily. Its nice if you have to quickly turn off the game and dont feel like having to go through something again.

However if you save at an owl, turn the game on, and then turn it off with out saving a second time, you will lose all progress. Well not entirly true, if you got a mask or an item and save at the owl, you will still beable to keep it even if you do not save for a second time.

However you will start at day 1 again...

If this is to confusing, just read the warning before you get to save at the owl.

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[original looks better, but the site wont allow its awsomeness, so i had to shrink it a bit]