I think of it as a bucket into which I can put money.
Within that bucket, I could have cash, or stocks, or bonds, or a mixture. And I could store that bucket at a bank, or at a mutual fund company.
If you hold it at a bank, and only put cash in there, then it would be more like a standard bank savings account. You'd earn some (low) amount of interest, which would grow tax-free until it is time to take the money out in retirement. With a regular bank savings account, you declare your interest to the IRS as part of your earnings each year. With an IRA you don't have to pay tax each year. But if it's a traditional IRA you have to declare the amount of money you take out as income, and pay tax at that point. If it's a Roth IRA, the withdrawals are tax free as you used after-tax income to fund it.
If you hold it at a mutual fund, you can put the money into various funds, and it would operate very much like your 401k.