It wouldn't have to improve existing schools.
One of the major advantages to having a voucher system in public education is that it creates a competitive marketplace for schooling. But that means several things:
1) It allows parents to select the school of their choice, rather than being assigned a school and told that they need to send their children there regardless of the condition of that school.
2) It allows schools to develop specific focuses for different markets - music, athletics, computing, machinery, whatever. Parents and students who have an interest in a particular topic will be able to pool resources in order to see schools that serve those interests established.
3) Parents are able to, if a school fails their children, move to another school. Currently, public schools can write off a certain number of students, because the only evaluation that matters is the one that comes from the government. Parents who want to see their children educated and complain to a school can, in effect, be told to take a hike without recourse.
4) Schools that failed to serve the needs of their students would be bankrupted by mass defections. While the modern public school could even announce that they've written off specific students with limited repercussions, under a voucher system such a school would be compelled to close after being abandoned.