It means that your “need” is determined, and the college covers all of it with financial aid, with at most a small amount of student work and student loan expectation.
However, the big variable is how “need” is determined, which varies widely between different colleges, resulting in very different amounts of financial and and net price. You need to try the net price calculator on each college’s web site to get an estimate. An additional warning is that if the net price calculator does not specifically ask questions that determine international student status, you need to check with the college whether international students will get the same level of financial aid as domestic students.
You probably do not want to put a number higher than the lowest expected parent contribution from any college’s net price calculator, if your goal is to maximize offered financial aid. (May differ if applying to need-aware colleges.)