Depends. You don't pay tax on inherited property, except qualified monies, ie. IRAs.
If the annuity is a traditional IRA, then the money is taxed when withdrawn. There are rules for when you must withdraw funds from an inherited IRA, annuity or otherwise.
If the annuity is non-qualified, not an IRA, then only the gain is taxed when withdrawn. If you annuitize, also known as taking an income stream, the taxable portion is prorated with tax-free return of principle.
If you take money out without annuitizing, all the taxable profit comes out first, then principle.
Example: Annuity has $100,000 of which $20,000 is gain.
If you don't annuitize, the $20,000 taxable profit comes out first.
If you annuitize, 80% of each payment is a return of principle and 20% is taxable gain.
Hope this helps.