Meaning
Can you believe it? / Is that even possible?
Example
O cara cobrou cem reais por um café. Tem base?
The guy charged a hundred reais for a coffee. Can you believe it?
Origin
The defining Goiano interjection of disbelief — literally 'is there any basis?'. Studied since 2003 by the Grupo de Estudos Funcionalistas of the Universidade Federal de Goiás (UFG), it's so identified with the state that it appears on flags and t-shirts as a marker of regional identity.
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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