Targum means translation. The best-known are Onkeloss Aramaic translation of the Torah, and the Targum Yonatan of the books of the prophets.
Traditionally, the public Torah-reading on Shabbat would be accompanied by verse-by-verse translation into the Aramaic vernacular, rendered by a functionary called the torgaman, the official translator.
Until recently, this was still the practice in Yemenite communities.
Interestingly, the root of the word targum appears to be ragam, meaning to project an object (especially a stone.) This is parallel to the derivation of the word translate, which means to bear across,to move from one domain to another.
Judaism has an intensely ambivalent attitude to translation of its sacred texts. The public translation of the Torah reflected the importance of the Jewish masses understanding what they heard. On the other hand, the rabbis were aware that something is always lost in translation.
Whole religions have been nourished by misunderstandings that have sprouted from accidental or deliberate mistranslations of the Torah into Greek or Latin.
The Talmud (Megillah 3a) reports that when Yonatan Ben Uziel translated the books of the prophets, the ground shuddered across an area of 400 parsangs and a heavenly voice demanded to know why esoteric secrets were thus being revealed. Yonatan replied that he had acted only for Gods honour so that the meaning of the prophets should be made unambiguously clear.
Rabbi Abraham Isaac Kook (1865-1935) noted that the gematria (numerical equivalent) of targum is tardemah, meaning slumber.
ArtScroll and others have helped to spread Jewish knowledge through the translation of the Talmud and other sources, but Torah study in English misses much, as if we were half-asleep.