Traditional IRA contributions

I was under the impression that you could contribute funds to an Trad IRA and claim those contribution via your tax filings, and that contribution would reduce your tax burden. But come to find out that if you have a company provided pension plan, you can't contribute as the system (TurboTax) will indicate you can't claim the contributions. Is this correct? If so, then what's the benefit of an IRA, since the money applied are earned money after taxes (like from savings or other funds) and wish to increase its value and reduce tax burden - this doesn't make sense. Why have a Trad IRA then, and just use a regular savings account.