To be worth my while means that something is important enough to justify the amount of time or work that one must do to achieve it. Another common idiom that contains this expression is to make something worth your while. People use this when they wish to compensate a person well for taking some action.

What does worth your while mean?

make something worth one's while. Compensate one for one's time or efforts, as in If you take care of our yard while we're away, I'll make it worth your while. [Mid-1800s] Both usages employ while in the sense of “a period of time spent.”

Is it worth while or worth the while?

In terms of meaning, there is no difference between the two words. When you say that something was 'worthwhile', you mean that the time, money or energy you spent on it was worth it. In other words, you are quite happy with the result.