The Eligibility in the Local Context means that your child, when applying to UCs, is guaranteed a spot in a UC that has room if he or she does not get into any other UC. Right now, that school is Merced.
The ELC determines which of your child’s A-G courses taken in 10th and 11th grades, meets the requirements.
http://admission.universityofcalifornia.edu/freshman/california-residents/local-path/index.html
If your child was missing any A-G courses before senior year, and/or had a smaller number of students in her class, then she might not be “ELC eligible”.
ELC just basically means she can go to Merced.