Very quick and simple answers to get you started:
A Money Market fund is typically a checking/savings type account that pays interest on the money you deposit. It's a good place to keep cash you might need immediate access to, like your emergency fund. They're a safe place to stash cash you plan to or may need in the near future (like when you're saving up for the down payment on a house, for instance, as well as your emergency fund), but carry lower interest rates than longer-term investments.
A CD is a Certificate of Deposit, a short or medium-term investment (I think the shortest are 3 months, and you can get them for terms of up to a few years.) They'll earn a higher rate of return than liquid accounts (like the money market fund), but your money is tied up until the CD reaches maturity, unless you're willing to pay a penalty for early withdrawal. They're a good place to stash money you know you won't need immediately, but will need at a specific point in time not too far in the future (like if you have a child who will be starting college in a few years, for instance.)
An IRA is an Individual Retirement Account. You can contribute up to $4000/yr, currently, to an IRA. If you meet the income requirements for a Roth (adjusted gross income under $150k) I'd recommend a Roth IRA, because taxes are paid on contributions, but your earnings (as long as you follow the rules) aren't taxed at all. With a traditional IRA, you can get a tax deduction for contributions to your account, if you qualify, but you have to pay taxes on the earnings. If you can possibly afford to, you should definitely max out your IRA contribution every year, because there's no way to make up for years you didn't contribute, and the power of compounding works in your interest when the money has years and years to sit. The money is tied up until retirement age, though, unless you pay a penalty for early withdrawal (and the penalties are pretty hefty.)
A 401k (or 403b -- same thing, but for nonprofit organizations like universities) is sort of like an IRA, but sponsored by an employer, and with a much higher contribution limit. Some employers offer an "employer match", which means they'll match the first 3-6% of your income that you devote to the 401k. The funds get taken out of your paychecks throughout the year, and you don't get taxed on the money -- it's deducted from your gross income. It's a great way to save money on taxes AND save for retirement. If you qualify for one and you can possibly afford it, I highly recommend contributing the maximum allowed to your 401k or 403b. Like an IRA, though, the money is tied up until retirement. You *can* cash it out if you change jobs, but you'll pay penalties on the income if you do, and you can't reinvest it in such a great tax-sheltered way.
Hope that helps
Edited to add: forgot the 'what would you recommend' part
I'd start with funding the 401k/403b if you qualify for one, especially if there's an employer match. If there is an employer match, contribute at least enough to get the maximum match. And if you don't have an emergency fund, start building one.
After that, if you can fully fund the 401k and still have some left over, fund a Roth IRA if you qualify for one, or a Traditional IRA if you don't qualify for a Roth. One neat thing about these is that you can make a contribution for the previous calendar year up until April 15 of the current year -- so if you can't scrape up your full contribution by Dec. 31 of this year, you still have until April 15 of 2006 to keep working on it.
After that... well, if you've fully funded the 401k and the IRA, and have 6 months of living expenses set aside in a money market account in case of emergency, you're already doing *great* for 24 years old
But if you still have some left at that point, there are a number of things you can do. If you're saving up for a major purchase, like a house, you might want to go the CD route. If you have kids, I'd put money into a 529 for them. Otherwise, I'd put the rest into a good low-fee, no-load index fund, which is a fund designed to emulate the performance of an entire group of stocks -- the entire S&P500, for instance. You'll have a much lower risk and much lower fees than with purchasing individual stocks, and it's much easier because you don't have to do all the legwork required to make smart individual stock choices (which don't always do what's expected, even when all of the indicators are good.)
Hope that helps