15% institutional quota means that in all the colleges under NEET, There will be 15% seats of the respective institution reserved for you. The other 85% will be reserved for state.
For eg. If there are 100 seats in a college:
Case 1: If your college is in the same state as yours.
Now if you give NEET, you will be eligible for 15 seats of the college and even people from all over India will be eligible for those 15 seats. Now as you are a resident of that state, you will also be eligible for the other 85 seats. The counseling for the 15 seats will be online on the mcc site and for those 85 seats, after the state merit list comes out, your state will conduct the counseling seperately.
Case 2: If your college is in a different state than yours.
You will only be eligible for 15 seats of the college and counseling will be online on the mcc site.
Riya Tyagi, Doctor in making
Source: Quora Digest