A tax credit is money the government gives to you.
A tax deduction is money that the government won't tax.
Tax credits are more valuable than tax deductions. Here's a fantasy example of how a tax credit works.
Once upon a time, in one year, you earned $1000. The IRS said they would take 1% or $10 of that in taxes. However, you purchased a tent to live in, and the government was giving a $1 tax credit for tent dwellers. (Assume the tent was really cheap, too.) That tax credit is applied to your taxes... and your final tax bill is $9! The $1 tax credit was given to you.
Here's a similar story about a tax deduction.
The next year, you earn $1000, and the tax is the same: 1%, which is $10. However, you just bought a skateboard for $100, and the government is allowing skateboarders to deduct the cost of a skateboard because it's basic transportation. So, you have a $100 deduction! A deduction is subtracted from your taxable income. That means your taxable income drops to $900. Taxes are 1%, so, your tax bill this year is $9. (Same as last year!)
Notice how in the first example, you spent almost nothing, and got at $1 tax credit, and your tax bill was $9.
In the second example, you spent $100, and got a deduction, and then your tax bill was $9.
The tax deduction was like a $1 off coupon on that skateboard. So, thanks to that deduction, your $100 board really only cost $99. Whoop-de-do.
It's much better to do things that get you tax credits, than to do things that get you tax deductions.
It's even worse
Yes, it's even worse than the little stories. To get some itemized deductions, your spending must exceed some threshold, and usually that threshold is several hundreds to a few thousand dollars.
Also, my examples were totally unrealistic. Taxes are a lot higher - in the range from 10% to 38% - and incomes are a lot higher. The numbers were chosen to make a point: that tax credits are $$$ in your pocket, while tax deductions are like discounts for spending money in specific ways.
An alternative calculation
Another way to look at the examples is to say that a $1 tax credit is equal to a $100 tax deduction.
If taxes were higher than the example it's not so drastic. At the 25% tax bracket, a $1 tax credit is equal to a $4 tax deduction. A $1,000 tax credit is like a $4,000 tax deduction.
The $8,000 homebuyer credit is equal to a $32,000 deduction. (Another way to say it is: if you buy a house, you're not going to pay much or any income tax.)
Also published at AC: Comparing a Tax Credit with a Tax Deduction.