I'm sorry for your loss. Upon the death of a taxpayer, a new taxpaying entity—the taxpayer's estate—is born to make sure no taxable income falls through the cracks. Generally, income is taxed either on the taxpayer's final return, on the return of the beneficiary who acquires the right to receive the income, or if the estate receives $600 or more of income, on the estate's income tax return.
If his only income was social security then it is unlikely that you need to file an estate tax return. Please see this article with information that will help you determine your next steps. Death in the Family