Why shouldn't I just keep my money in the savings account and earn the same amount (both accounts have the same APY in this case)?
I will assume that you are transferring money from your savings account into
a Traditional IRA and deducting the contribution from your income. While
you may think that the money that is being transferred is yours already --
it is sitting in your savings account, for Pete's sake! -- you are deducting
that amount in getting to your taxable income, and so you are effectively
contributing it from current income and not paying taxes on the amount
contributed.
So, consider the same amount of money sitting in your savings account
versus the same amount of money sitting in your Traditional IRA account.
While you will earn the same amount of interest in both accounts, you will have
to pay taxes each year on the interest earned in the savings account. You might
choose, as most people do, to not take money out of the savings account to pay theses
taxes but just pay them from ready cash/checking account/current income etc., or these
taxes might just reduce the refund that you will getting from the IRS and your
State income tax authority, but in either case, you have paid taxes on the interest
earned in your non-IRA savings account, and of course, long ago, you also
paid taxes on the original amount in the non-IRA savings account. So, if you
take any money out of the non-IRA savings account, you don't pay any taxes
on the amount withdrawn except possibly for the interest earned from January 1
till the date of withdrawal (which you are paying from ready cash).
On the other hand, consider the Traditional IRA. The original deposit was not
taxed in the sense that you got a deduction (reduced tax or increased refund)
when you made the contribution. The annual interest earned was not taxed each
year either. So when you make a qualified withdrawal (after age 59.5 or
by meeting one of the other exceptions allowing withdrawal before age 59.5),
you are taking money on which you have not paid any taxes at all, and the
IRS wants its cut. The money withdrawn is taxable income to you.
Furthermore, the money withdrawn is not
eligible for any kind of favorable treatment such as having it count as
qualified dividends or as long-term capital gains even if your IRA
was invested in stocks and the money in the account is all qualified
dividends or long-term capital gains. If you make an unqualified
withdrawal, you owe a penalty (technically named an excise tax)
in addition to income tax on the amount withdrawn.
If you are investing in a Roth IRA, you will not be getting a deduction
when you make the contribution, and qualified withdrawals are
completely tax-free, and so the answer is completely different
from the above.