MP3's are just a different file format, and now-a-days most new CD players can also play what is called an MP3 CD, this is most likely what you were told about. These MP3 CDs are not sold in stores, as most albums only contain 10-15 songs, which is a complete waste for an MP3 CD. You can also purchase mobile MP3 Players that store the MP3 songs on the player without the need for a CD. A common example (As mentioned above) is the iPod. The iPod is basically a Hard Drive in a case. There are also MP3 players that use miniature "flash" cards instead of hard drives. These players offer longer battery life, as there are no moving parts in them (as opposed to iPod like players). To make an MP3 CD, you need to either download songs (Legal ones of course) or use a Media player like Windows Media Player or iTunes to Rip your CDs onto your computer as compressed MP3 files. With those players you can often choose an alternate file format that each player advertises, such as WMA and AAC, but you should stick to MP3s, since they have the largest compatibility, and the quality difference between the various formats is pretty much negligable. Once you have the MP3s on your computer, you use a burning program such as NERO or Roxio Easy CD Creator. You have several options. The easiest way is to use the "Wizzard" to make an MP3 Audio CD, this will walk you through the process. Alternatively, if your Burning program does not have a "wizzard", you can choose "Data CD", and just select all the MP3's you want to have and "Add" them to the CD. This might sound odd since you want an audio CD, but basically an MP3 CD is just a Data CD with MP3s on them. Once you've burned that CD, it will play in any CD player that supports MP3 music files. It should also work on most Stand-alone DVD Players (Like the one ontop of your TV in the living room), as most often they support MP3s as well. If you plan to listen to them on your entertainment system in your living room using the DVD player, you can alternatively create an MP3 Audio DVD, which is essentially a Data DVD with all your MP3s on it. Since a CD can hold only 700 MB, Versus 4.35 GB (The label says 4.7 GB, but you only actually get 4.35, sort of like how an 80GB Hard drive isn't actually 80 GB), if you are ONLY using it on your DVD player, the DVD is a better idea since it can hold vastly more amounts of MP3s (A few thousand). If you plan to listen to your MP3s on portable CD Players, using the MP3 CD is the appropriate way.
Hopefully that explains everything. If you plan to buy a mobile MP3 Player, they come with programs that will convert your CDs to MP3s and will walk you through the process of getting them on the player.