You reduce something when you lessen its volume, size, or degree. That's why we say when someone goes on a diet, it's because they want to reduce; it's a polite way of suggesting they need to drop pounds and become a smaller size.
The word reduce first appeared in Old French during the 14th Century, when it meant "bring back." From the Latin re, which meant "back," coupled with ducere, meaning "bring or lead" — we ended up with reduce. The current meaning, "to lessen," appeared in the late 1700's, drawn from the word's military use, "reduce to ranks," which meant break into smaller units. Cooks use the word reduce when they reduce a liquid, boiling it down until it has less volume and is thicker.