"Narrowing down" a list means to get rid of some of the items on the list. "Narrowing down" a list is usually considered to be a good thing, because it makes it easier for you to make a decision when there are fewer choices.
Here are some of the words most commonly used after "narrow down":
- narrow down a list
- narrow down your choices
- narrow down the suspects (of a crime)
- narrow down the possibilities