Bounded variation

Bounded variation means that something does not change too much. Imagine one line that stays pretty flat - that line is said to have bounded variation. It doesn't go up and down, or change too much. It just stays pretty flat. Now, imagine another line that goes up and down a lot - it keeps changing, going up and down like a roller coaster. That line is said to have unbounded variation because it keeps changing, or varying, a lot.