The laughter in this verse is the laughter of pure joy. This contrasts the laughter that Sarah had in 18:12-15 which is a laugh of skepticism and doubt.
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Explanation posted by John Wesley on 2007-01-01 00:00:00
And Sarah said, God has made me to laugh - He hath given me both cause to rejoice, and a heart to rejoice. And it adds to the comfort of any mercy to have our friends rejoice with us in it, See Luke i, 58. They that hear will laugh with me - Others will rejoice in this instance of God's power and goodness, and be encouraged to trust in him.