Meaning
To get the job done / To handle it
Example
Pode deixar comigo, eu dou conta do recado!
Leave it to me, I'll get the job done!
Origin
'Conta do recado' = the count of the message. The person who delivers on a task gets the job done.
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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