The literal German meaning is something like leading or central (the leit) part, with the motiv or motif part referring to some element, such as a short melodic phrase that is consistently used as a reference to a character or other element in a musical work.
The term was first coined in 1878 by Wagner's friend, man of letters Hans von Wolzogen, in an essay about the materials in the opera Göttedamerung. While Wagner was the first to consistently use this device (which he called Grundthema), other were known to use it in earlier 18th-century works.