According to the old rhyme from which this saying comes, a Thursday's child has far to go. This usually means that you will achieve a lot, go on a long journey either physically or in your spiritual or career development. It is generally considered one of the more positive days in the old rhyme - unlike Wednesday's child (full of woe) or even Saturday (working hard for a living - positive in a way but not much fun!)

You can find the full rhyme here.

The ideas of this old rhymes have sometimes been used in fiction. For example, I well remember a children's story entitled Thursday's Child, about an orphan girl who is found on the church steps as a baby (on a Thursday, of course) and who becomes a real 'Thursday's child' by having a number of adventures and starting on a career as a child actress.