Financial Need is the difference between the Cost Of Attendance (COA) at a school and your Expected Family Contribution (EFC). While COA varies from school to school, your EFC does not change based on the school you attend.
Below demonstrates how Financial Need is calculated:
Cost of Attendace (COA) - Expected Family Contribution (EFC) = Financial Need
Students with more Financial Need, typically can qualify for need based funding such as a subsidized stafford loan. Generally, students with more need also qualify for more institutional grant funding. Filling out your FAFSA early increases your chances for being awarded need based funding while the government's fund is still plentiful. Even if there is high need, filing the FAFSA late can potentially cost you grant funding you really need.