Pension is a benefit that an employee gets post-retirement. If this retirement benefit is passed on to the dependent family members, after death of the employee then it is called family pension.
Here is an example:
Arjun retires from his job as a branch manager at a state-owned bank. He receives INR 25,000 a month as pension from his employer. In this case, he needs to file ITR 1 and show Pension under the Income Head Salary.
Arjun passes after 3 years, his pension amount will be now transferred to his wife, this is called family pension. His wife needs to file ITR 1 and show the Family Pension income under the head Income from Other Sources.