Pension is a benefit that an employee receives after his/her 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:

Case 1: Pension

Arjun retires from his job as a branch manager at a state-owned bank. He receives INR 25,000 per month as pension from his employer. In this case, he needs to file ITR 1 and show Pension under the Income Head Salary.

Case 2: Family Pension 

Arjun passes away after an year as a branch manager. Then, his pension amount will be transferred to his wife which is termed as family pension. His wife is now liable to show the Family Pension income under the head Income from Other Sources.