In relation to American history, "The Age of Jackson" and "The Age of the Common Man" are virtually synonymous. Andrew Jackson saw himself and his Democratic Party as representing the interests of the common man, protecting them from exploitation at the hands of the East coast banking and commercial elite.
Under Jackson's presidency the political system opened up to people from a much wider range of social backgrounds. The new spoils system—giving government jobs to Jackson's supporters—was hugely controversial, not least because it tacitly encouraged graft and corruption. Nevertheless, it did open up the civil service to people who ordinarily wouldn't have been given the chance to serve in government. In that sense, one could say that the change in the social make-up of the federal government was a prime illustration of this new age, The Age of the Common Man.
Jackson's implacable hostility to the renewal of the Second Bank of the United States' charter can also be seen as in keeping with the prevailing ethos of the age. In common with fellow Democrats, Jackson believed that the Second Bank existed to serve the interests of commerce and finance, and not those of the landowners and small businessmen who formed the backbone of Jackson's election-winning coalition. So when the Second Bank's charter came up for renewal, Jackson vetoed a bill that would've extended its life. In doing so, he gained extra support among ordinary Americans, who believed that a centralized banking system was not in their economic interests.