A "mischievous mite from another dimension" (Detective Comics No. 276, Feb 1960: "The Return of Bat-Mite!")--endowed with extraordinary extradimensional powers similar to if not identical to those possessed by the incredible Mr. Mxyzptlk--who looks like "an elf dressed in a crazy-looking Batman costume!" (Detective Comics No. 267, May 1959: "Batman meets Bat-Mite!"). Although Robin has called him an "imp" and a "gremlin" and Batman has called him a "pest" (Detective Comics No. 267, May 1959: "Batman meets Bat-Mite!"), Bat-Mite sees himself only as Batman's "greatest fan" and his periodic visits to the earthly dimension as exciting opportunities to "see [his] favorite crime-fighting hero in spectacular action..." (Batman No. 161/2, Feb 1964: "The Bat-Mite Hero!").
To ensure that the action he sees will indeed be "spectacular," Bat-Mite uses his extraordinary extradimensional powers to prolong and enliven Batman's battles with the underworld, thus forcing the Dynamic Duo to ever greater heights of skill and ingenuity, as when he intentionally endows three small-time criminals with superhuman powers so that "Batman and Robin [will] have to use sensational tricks to defeat them!" (Detective Comics No. 310, Dec 1962: "Bat-Mite's Super-Circus!").
In November 1960 (WF No. 113: "Bat-Mite Meets Mr. Mxyzptlk!"), February 1962 (WF No. 123: "The Incredible Team of Bat-Mite and Mr. Mxyzptlk!"), and again in September 1965 (WF No. 152: "The Colossal Kids! pts. I-II--no title; "The Magic of Bat-Mite and Mr. Mxyzptlk!"), Bat-Mite visits the earthly dimension for a series of encounters with the mischievous Mr. Mxyzptlk. (TGSB)