My friend got this tattoo like 6 years ago and he can't remember exactly what it means.
天上天下 (above and below the Heaven) is a Japanese phrase, The whole phrase is "天上天下唯我独尊" (I am the only master above and below the Heaven)-- Quite a statement for a tattoo
originally, "I am the only master above and below the heaven" is not what Buddha said
It was also used as a title of a famous Japanese manga by Oh Great
Similar Chinese phrases include 天下, 天上地下 and 上天下地
"天上" means above the sky(or heaven). "天下" means below the sky(or heaven).
The original phrase may be "天上天下，为我独尊。", or it may also be "天上天下靡有逾我者" from @user6065's comment.
@Tang Ho already pointed out that "天上天下，为我独尊。" means "I am the only master above and below the heaven".
"天上天下靡有逾我者" has very similar meaning. "靡(mǐ)有" means "没有(no, there is not). "逾(yú)" means "超过(to exceed)". So this entire phrase means "There is no one(者) exceeds me(我) above and below the sky(or heaven)".
But there is no evidence to prove Gautama Buddha was the original person who said this phrase. 芒果侠's answer pointed out that Gautama Buddha did not say this.
Since books of Buddhism are mostly written in Sanskrit and there could be thousands of different versions of translations in Chinese language. There is no clear clue of who said this phrase.