A lower court is a court that has the ability to allow an appeal on a case that is heard. Appeals can be taken to a higher court and continue appealing until the case reaches the Supreme Court if necessary. The Supreme Court does not have the ability to be appealed, but any court that is lower has that ability.
When a case is appealed in a lower court, it could be heard again in that court or in a comparative-level court, or could be sent up the ladder to a higher court.