Test cases is nothing but a condition, this will be used for testing.It will be better if i explain it through an eg. If someone asks u to test an application , say some site and users below 18 years are not allowed.Then we an create test cases as follows:

age<18;
age=18 ;(boundary level test casesare important, since it may fail many times)

age>18;

All these are test cases to check whether our application is working according to need or not. Test cases are ground on which we perform testing.