This phrase is used when you want something to happen, but you don't think it's very likely.

People often mix up "I wish..." and "I hope..." The difference is in how realistic your wish is. For something that's not very likely, or is impossible, use "I wish..."

I wish I could fly.

Or you can talk about changing the past:

I wish I'd studied something a little more practical.

For something that hasn't happened yet, but might still happen, use "I hope..." For example, if the weather forecast calls for rain, you can say this before the rain starts:

I hope it doesn't rain.

This is OK because it's still possible that the rain won't start. After the rain starts, you can't say that but you can say:

I hope it stops raining soon.

* For more about the difference between "I hope" and "I wish", read this article: How should I use "I hope" and "I wish"?