The Ohr ha-Hamah (R. Zundel Kroizer) on Psalms 88:1 writes:
ע"י תורגמן אמרו ואין מבואר מה ענינו של תורגמן בזה ואפשר דכל מזמור שהוא
חשוב לכל העם ורצה שכולם ישמעוהו העמיד מתורגמן שישמיע את המזמור הזה
לרבים וכדוגמא מה שהיה נהוג בימי האמוראים שכל רב שהיה רוצה להשמיע העמיד
אמורא לפניו מה שהוא לחש לו בשקט
By means of a turgeman they [i.e. the Sages] said. And it isn't
entirely evident what the purpose of this turgeman was. It could be
that each psalm that was important for the nation, he wanted everyone
to hear it, so he appointed a meturgeman to cause it to be heard by
the masses. Similarly, during the Amoraic era if a Rabh wanted to be
heard, he appointed a meturgeman before the Amora to cause to be
heard what he had whispered quietly to him.
The Ohr ha-Hamah here suggests that the meturgeman is utilized as an amplifier and interpreter of the original speaker. He analogizes it to the Amoraic institution of the meturgeman which the Jewish Encyclopedia describes as follows:
The head of the academy, while seated, would tell him in Hebrew and in
a low voice the outline of his lecture; and the meturgeman would in a
lengthy popular discourse explain it in the vernacular to the
audience.
R. Adin Steinsaltz takes a similar tact, and explains Pesahim 117a as follows:
אם המזמור מתחיל בלשון "משכיל" — כוונתו שאמרו על ידי תורגמן, שנאמר
לרבים כעין דרשה. שהוא אמרו כדרשן הדורש בלחש, והמתורגמן אמרו ופירשו
ברבים
If a psalm begins with the language of "maskil" - the intention is
that it was said by means of an interpreter (meturgeman) that was said
to the masses like a homily. And it is said by the homiletician as a
whispered homily and the interpreter says and explains it to the
masses.
According to this understanding, the source language is a technical language accessible to the wise and their adepts, and the target language is the common vernacular of the masses. It isn't quite that Hebrew was being translated into an altogether different language (such as Aramaic), rather it was being translated from a less accessible form to a more accessible one. By analogy, different professions have their own "lingo" - they aren't exactly speaking a different language, but it may as well be if one isn't initiated to the respective field. Its kind of like the meturgeman gives the TED-Talk version of the psalm for the benefit of the masses.
