Suppose you have an existing A line with 1500 riders and you're considering building a B line, but you need 1000 riders to justify it and you predict there will only be 900, so you don't build it. However, if you eliminated fares then you might expect 1100 riders for the B line. Then the lack of fares also gives you another 300 riders for the A line, and the existence of the B line gives you another 600 riders for the A line since then people can then go from A to B. So eliminating fares allows you to build the B line and add 2000 riders across the two lines, even though only 500 of them were directly from the elimination of fares.

And you get a much better incentive for ridership when you go from something like $1 to zero than you would from, say, $2 to $1, because it increases convenience. You don't have to worry about tickets or exact change or anything, you just go through the door and you're on your way.