Approbation is a formal word for approval or praise. Approbation is like getting the nod in a big way. Politicians rely on the public’s approbation to get elected.
How is it possible that approbation means approval when probation is a form of being in trouble? Probation is a testing period, to see if you can be good. Approbation means it's all good. Or you can remember this rhyme: "Filled with approbation, the audience gave a standing ovation."