It accomplishes a ton:
* It gets people who cannot afford regular fares to use these services when appropriate, rather than what might be less desirable (having a friend drive them around if they are too poor, etc).
* It gets people using services they might not use otherwise. A lot of commuters would take the train once or twice just because its free. If you can get people started on using public transit, they might just keep using it.
* You can also give away free rides during low density hours, such as at night. This can help offset daytime load by getting people to do their time-flexible commutes at off hours.
Now there are a lot of tweaks on the model, like making free rides only eligible for non-peak hours. But the whole point of public transit is to increase the efficiency of people and business in the economy where it is built - it is never meant to turn a profit, and if it is profitable it is probably failing on that first premise by costing so much to use. Making it completely free all the time makes it rife for abuse unless you institute a system where riders who ride the most get the least priority. But honestly if anyone were willing to implement such a system making the transit free and just using the tax revenue of booming business to pay for the transit is a much more sensible model than trying to keep your transit system revenue neutral or even cash positive (cough, Amtrak).