Meaning
To shoot the breeze / To make small talk
Example
Não tinha nada para fazer, fiquei jogando conversa fora com a Rita.
I had nothing to do, I was shooting the breeze with Rita.
Origin
The image turns on the verb jogar fora, "to throw away". A conversa fora is talk with no aim — not meant to settle anything, just enjoyed for its own sake — so it is light enough to be "thrown out".
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity