The verb mull means to think deeply about something, the way you might mull over your choice of what college to attend.
When you mull something over, you ponder or seriously consider it. You could mull over what aid organization to donate money to following a natural disaster, or mull over what to study in college. People are most likely to mull over important decisions, but you can use the word mull, almost always with over, any time you're giving serious consideration to something. A completely different meaning of mull is "to heat, sweeten, and spice," as when you make mulled cider.