The main reasons are that investment are deducted from your gross income and earnings are not taxed until withdrawal. This applies to both traditional IRAs and 401Ks. Roth accounts have different rules but valuable benefits.
Income tax deferral on contributions
My effective income tax rate is around 35%. This means that for every $1000 I earn in wage I only get to keep $650. Since my 401K contributions are deferred reductions from my income I can invest 35% more money into my 401K than I would be able to invest in a non-tax-advantaged account. Where I can invest $1000 into my 401K I would only be able to invest $650 into a non-advantaged account with the same wages.
If I put $650 into an account yielding 10% then my one-year return on my income is $65
The 10% return on my $1000 is $100. Compared to what I would have been able to take home in the first place this makes my ROI $100/$650 = 15.3%
Tax deferral on earnings
Interest earned in non-advantaged accounts incurs taxes every year. Interest earned in advantaged accounts does not incur taxes until withdrawn.
Compounding 10% annually for 20 years is significantly more than 6.5% compounded annually for 20 years.
Imagine 10% on a 1000 investment with no additional cash flows over 20 year. The result is $6727, or 672%. Imagine your income tax rate does not reduce below 35%, your after-tax return is 4372, or %437 return.
Now imagine you pay taxes every year on 10% take, so your take annually is only 6.5%... Now over 20 years you have $3523 (but you've already paid all taxes on this) and your return is %352
You have earned 24% more money because taxes were deferred until withdrawal!
EDIT: Some tabular info for the commenters
+-------------+-------------+-------------+
| P | G | N(LESS 35%) |
+-------------+-------------+-------------+
| | | |
| 1000 | 1100 | 1065 |
| | | |
| 1065 | 1171.5 | 1134.225 |
| | | |
| 1134.225 | 1247.6475 | 1207.949625 |
| | | |
| 1207.949625 | 1328.744588 | 1286.466351 |
| | | |
| 1286.466351 | 1415.112986 | 1370.086663 |
| | | |
| 1370.086663 | 1507.09533 | 1459.142297 |
| | | |
| 1459.142297 | 1605.056526 | 1553.986546 |
| | | |
| 1553.986546 | 1709.3852 | 1654.995671 |
| | | |
| 1654.995671 | 1820.495238 | 1762.57039 |
| | | |
| 1762.57039 | 1938.827429 | 1877.137465 |
| | | |
| 1877.137465 | 2064.851212 | 1999.151401 |
| | | |
| 1999.151401 | 2199.066541 | 2129.096242 |
| | | |
| 2129.096242 | 2342.005866 | 2267.487497 |
| | | |
| 2267.487497 | 2494.236247 | 2414.874185 |
| | | |
| 2414.874185 | 2656.361603 | 2571.841007 |
| | | |
| 2571.841007 | 2829.025107 | 2739.010672 |
| | | |
| 2739.010672 | 3012.911739 | 2917.046366 |
| | | |
| 2917.046366 | 3208.751002 | 3106.654379 |
| | | |
| 3106.654379 | 3417.319817 | 3308.586914 |
| | | |
| 3308.586914 | 3639.445606 | 3523.645064 |
| | | |
| 3523.645064 | 3876.00957 | 3752.681993 |
+-------------+-------------+-------------+
Your take home from the investment is $3752 because you have diligently paid your taxes every year on the earnings.
Now, with the tax deferred until withdrawal!
+-------------+-------------+-------------+
| P | G | N(NO TAX) |
+-------------+-------------+-------------+
| | | |
| 1000 | 1100 | 1100 |
| | | |
| 1100 | 1210 | 1210 |
| | | |
| 1210 | 1331 | 1331 |
| | | |
| 1331 | 1464.1 | 1464.1 |
| | | |
| 1464.1 | 1610.51 | 1610.51 |
| | | |
| 1610.51 | 1771.561 | 1771.561 |
| | | |
| 1771.561 | 1948.7171 | 1948.7171 |
| | | |
| 1948.7171 | 2143.58881 | 2143.58881 |
| | | |
| 2143.58881 | 2357.947691 | 2357.947691 |
| | | |
| 2357.947691 | 2593.74246 | 2593.74246 |
| | | |
| 2593.74246 | 2853.116706 | 2853.116706 |
| | | |
| 2853.116706 | 3138.428377 | 3138.428377 |
| | | |
| 3138.428377 | 3452.271214 | 3452.271214 |
| | | |
| 3452.271214 | 3797.498336 | 3797.498336 |
| | | |
| 3797.498336 | 4177.248169 | 4177.248169 |
| | | |
| 4177.248169 | 4594.972986 | 4594.972986 |
| | | |
| 4594.972986 | 5054.470285 | 5054.470285 |
| | | |
| 5054.470285 | 5559.917313 | 5559.917313 |
| | | |
| 5559.917313 | 6115.909045 | 6115.909045 |
| | | |
| 6115.909045 | 6727.499949 | 6727.499949 |
| | | |
| 6727.499949 | 7400.249944 | 7400.249944 |
+-------------+-------------+-------------+
You then owe 35% tax on the withdrawal so you keep 7400 * .65 = $4810
$4810 versus $3750 means you have made an additional $1060, or 28%, from the compounding against tax-advantaged earnings.
But Matthew! you say... Annual proceeds from your investments are not taxed at your income tax rate. This is true for now but the political winds are pushing this direction. However, even if you use a reduced rate in the first situation (let's say 30% instead of 35%, if you're a California resident) then the effect is $4140 rather than $3750. Less of a gain, but still a gain. In fact your capital-gains rate would have to be as low as 22% to even this difference out (versus a 35% income tax rate).... And remember that this assumes you're in the same bracket at retirement (which more people are not)
You may also note that I used $1000 as the principle in both calculations. This was intentional to show the effects of compounding the taxable earnings alone. If you replace the taxable principle with $650 instead of $1000 then the effect is even more pronounced and only balanced out if your capital gains rate is actually zero!