The origin is Old Norse hus-thing, “house meeting”, and referred to an assembly of the people in the household of a noble man or woman. Over time its meaning has come to mean a platform for politicians to make speeches from.
The thing element just meant assembly and survives today in the name of the Icelandic supreme parliament, the Alþingi.
Old English also had folk-moot, “folk meeting”. Here moot is the same as in the phrase “a moot point” = a point to be discussed and also found in moot hall. Folkmoot survives but mainly in historical contexts.