Living in a capitalist economy means that one's life path is largely dictated by getting money, spending money, and saving money. Most people are plenty good at spending money, and some people are pretty great at getting money, but few excel at saving money, mostly because saving money is boring, not fun, and not simple, but oh so necessary.
While the idea of saving money for the long term might seem ridiculous to someone who is just starting out and trying to live on ramen until their next paycheck, eventually, we'll all have to figure out how to put a little away for a rainy day, and even if you're not ready to start saving now, at the very least it's important to familiarize oneself with proper terminology so that you're capable of thinking about money using the vocabulary of money, saving, and investing.
401Ks, 403Bs, 457B, IRAs, and Roth IRAs are all types of accounts that are taxed differently. They are containers into which you place your assets that you're saving for the long term- stocks, bonds, mutual funds, options, cash, etc.
401Ks, 457Bs and 403Bs are accounts that you enroll in through your employer. 401Ks are for people who work at for-profit companies and 403Bs and 457Bs are for people who work at non-profit-generating entities, like schools or NPOs. You don't have a say in what type of plan your employer has; your employer sets it up. If you'd like to enroll in your employer's plan, ask HR if you're eligible and what you need to do. Once you've decided to invest in a specific type of account, then you make decisions about what type of investment strategy you'd like to employ. Plans like this generally have a bunch of options on how you'd like your money to be invested within your plan- if you're more conservative or aggressive or if you just want it all sitting there in cash. Usually, your choices will include a list of mutual funds that follow a specified investment strategy and you get to pick what percentage of your money goes where. If your eyes are crossing when you think about trying to parse through your investment choices, call the representative of the company that manages your 401K plan. They have someone there whose job it is to help people like you. Use them; you're paying for them.
Often (but not as much nowadays) companies will match your contribution up to a certain percentage of your income. This is basically additional compensation from your company, so even if the options within your plan are crappy, it makes sense to contribute at least to the company match (usually 3, 4, or 5%) so that you can take advantage of the free money they're offering you as incentive to save.
You don't pay taxes on money you contribute into a 401K until you take it out, and you can't take money out of your 401K until you're 55 years old (with stipulations) without substantial tax penalties (with rare exceptions, but for the purpose of this kind of brief explanation, I won't go into those).
The maximum amount you can contribute to your 401K in 2011 is $16,500. If you're over 55, you can pitch in an additional $5,500 as a "catch up" contribution.
If you find yourself in dire financial straits, you can access funds in your 401K without penalty, but this depends on the company that manages your plan. Most 401K plans will allow you to take a loan out against the value of your investments, but they have different rules on how you must pay yourself back.
If you quit your job, you may choose to roll your 401K into an IRA (Individual Retirement Account). An IRA is almost identical to a 401K, taxwise, except that the account is yours rather than part of a company plan, and so it could almost go without saying that there is no company match.
Not every company has a 401K, 403B or 457B plan. If your company doesn't, or if you don't have a job but you do have income, you can open your own IRA account. You can also open an IRA to supplement savings through your employer, or if you really don't like the options available to you through your employer's plan.
A Roth IRA is a retirement savings vehicle that's taxed differently than a regular IRA and that has different income requirements attached to it. If you're a single person making less than $107,000 per year or a married person whose household makes less than $169,000 per year, then you can contribute to a Roth IRA.
The difference between a Traditional IRA and a Roth IRA lies is where the investments are taxed. If you contribute to a traditional IRA, contributions are considered "pre-tax," and thus reduce your individual income tax burden in the year that you make the contribution. When the time comes to take money out of an IRA, you owe taxes based on your tax bracket in the year that you withdraw the funds. For example, if you earn $1000 and contribute $100 to a traditional IRA, you are taxed as though you earned $900, because the $100 you contributed to your IRA isn't taxed until you take it out in three decades or whatever amount of time needs to pass between now and when you retire. Roth IRA contributions are made with after-tax money, but when you withdraw money from a Roth IRA, you are not taxed. If you earn $1,000 but contribute $100 to a Roth IRA, you pay taxes on all $1,000, but when you retire, you never have to pay taxes on that $100 again. Thus, if you think you're going to be in a higher income tax bracket when you retire than you are now, it might make the most sense to contribute to a Roth IRA.
If you contribute to Traditional IRA, you may begin withdrawing funds at 59 1/2 and must begin withdrawing funds at 70 1/2. If you contribute to a Roth IRA, you may begin withdrawing funds at 59 1/2 and there is no age at which you must begin withdrawing funds.
Things get a little more complicated and there are other options if you own your own business or if you're self-employed or if you've figured out how to declare yourself an S-Corp (and if you have figured out how to incorporate yourself, please email me, as corporations seem to have more rights than individual citizens nowadays) but for the sake of simplicity, I won't go into them on this, the first day of trying to explain something very boring but necessary to readers.
Cliff's notes: A 401K is a type of employer-sponsored account into which you can deposit money that you plan on using after you retire. You don't pay taxes on the money in that account until you take it out. If your employer offers a 401K or 403B plan to its employees, there should be someone at the company that manages the 401K to help you make investment decisions. An IRA is an Individual Retirement Account that serves the same purpose as a 401K. A Roth IRA is another type of long-term investment vehicle.
Hopefully this was illuminating for the unfamiliar and not too tedious for those familiar with how American workers save for the long term. In the meantime, if you have any questions about simple personal finance type stuff, leave it in the comments and I'll see if I can rassle up some answers.
More information on Roth IRA's, Traditional IRA's, and 401K type plans.