EFC stands for Expected Family Contribution. The EFC is an index used by the financial aid office to determine how much aid may be eligible for. The EFC is calculated by the Department of Education based on the information submitted via the FAFSA. The calculation is done according to formula established by Federal law.
There are several factors taken into consideration in the calculation of the EFC, including but not limited to family size and income, assets, and the number of family members who may be attending college.
The EFC is not the amount of money that your family will need to come up with in order for you to attend school. It is merely an index, calculated by the Department of Education, used to determine eligibility for aid.
A more detailed explanation of what the EFC is can be found here.