お嬢様実力テスト means lady ability test, referring to an online test going viral on Twitter.

お嬢様 has been a term used to address a lady of a fine (or more narrowly, noble) family. 実力 means ability or strenghth, and テスト is the transliteration of “test”. So this お嬢様実力テスト is a test to decide if you have the ability of a fine lady. However, the only input to this test is a name, making it a pure entertaining test, which might explain why it goes viral. If one share the result from this test to Twitter, the post would include the tag お嬢様実力テスト, causing it to trend.

You can also try this test here (in Japanese only).