A traditional (pre-tax) IRA means you put the money in an account before taxes are taken, and then this money is allowed to grow tax free as long as it remains in the account. When you start to pull money out the money is treated as ordinary income (it's as if you're making a salary equal to the amount you withdraw). This is best if you expect your tax burden to be lower in retirement than they are currently (generally you expect to have a lower income in retirement). What this means is that you really own about 70% or so of whatever your balance is in a traditional IRA, with the government owning 30% or so they'll collect in taxes when you start making withdrawals.

A Roth (after tax) IRA means you the money you are putting in the account has already been taxed. You've already paid taxes on the money you put in, and any increase in value will also be tax free when you withdrawal it. If you think you will make more money in retirement, or tax burdens will increase (considering the spending of the government this is probably a good bet) the the Roth IRA is for you.

These comments are all based on the assumption that the government doesn't change its mind sometime in the future, and thinks that it is unfair for you to have saved for your retirement when other people did not. Every so often (and likely to increase as the government becomes more cash strapped) you'll hear whispers of the government wanting to tap these accounts--applying means testing or some other things. I think they're safe in the mid-term future, but if things get really bad I wouldn't be surprised if the government does what governments do and steals your money.

The mentions above are about the basic rules, but there are a bunch of other ones around how and when you can withdrawals, and some income tests for individual IRAs.