In the beginning of the 19th Century or 1800s, Democrats like Andrew Jackson supported states' rights and the power of the people. Jackson was in favor of getting rid of the National Bank because he felt it would give too much power to the wealthy and not the common man.
In the middle of the 1800s, Democrats like Stephen Douglas who battled Abraham Lincoln believed in allowing slavery to stay as long as the people got to vote for it (that was called popular sovereignty).
Republicans like Lincoln wanted to keep the Union or country together during the Civil War and keep a strong, central government. Lincoln and other Republicans also wanted to get rid of slavery.
In the late 1800s or 19th Century, Democrats still favored the common man or farmers. People like William Jennings Bryan in politics pushed for free silver, an eight hour workday, an income tax, and regulation of the railroads to help out the common man or farmer.
The Republicans in the late 1800s favored gold and the wealthy to have control of most things in government. They did not want much say or control from the common man.