Why was Andrew Jackson popular with voters in the South and West during the 1820s and 30s?
The general reason for this was that Jackson was a politician who was from the "common people" and who tried to cater to their needs and wishes.
Jackson was not from a privileged background like previous presidents had been. This endeared him to the backwoods people of the South and West. He also took policy positions that were popular with them. For example, he backed the removal of the Native Americans from what is now called the Southeast, thus pleasing people who wanted the land the Indians had occupied. He also fought against the Bank of the United States, which many Southerners and Westerners saw as an elite attempt to harm them.
For these reasons, Jackson was popular with these voters.