What do Katrina's fortunes mean (if anything)?

Katrina the fortuneteller in Animal Crossing: New Leaf often gives me a prediction of good or bad events, then tells me an item is the key to it.

Generally speaking, how do I decipher her prophecies?

Solution 1:

In New Leaf, Katrina inlcudes a wearable item in her fortunes. If you wear this item, it will increase your luck until 11 PM on that day.

Taken from Thonky's guide:

"In Animal Crossing: New Leaf, your luck is random every day. Different good or bad things can happen to you based on your current luck. There are 5 types of luck: money luck, friendship luck, love luck, item luck, physical luck. Each of these can be good or bad each day."

There's a lovely little chart about luck there as well.

http://www.thonky.com/animal-crossing-new-leaf/katrina/