One of the most common points of confusion I encounter with clients regards the difference between memory and storage. Many people use the term "memory" to refer to the space on their hard drive and view that space as what limits the software they can run as well as the amount of files they can store. This is NOT the case and memory is actually very different from STORAGE.
Here's the way I usually explain it...
Imagine that your computer is a desk that has a desktop and file drawers. The top of your desk determines the number of things you can work on at the same time - the bigger the desktop, the more projects and folders you can have in process at the same time. The drawers determine how many files and folders you can store. The more drawer space you have, the more files you may have - and drawers store files more compactly than the desktop, so you can store a lot more in a drawer than flat on top of the desk.
MEMORY is like the surface of your desk - the more you have, the more programs and files you may have open at the same time. Memory or "RAM" (for Random Access Memory) typically is measured in even units of Gigabytes (a Gigabyte or 1GB equals one Billion bytes - or roughly the size of 200 to 300 songs on iTunes!). Modern computers typically come with RAM of 2GB, 4GB, 8GB or even more. It's tough to have too much RAM - especially on laptops.
STORAGE is like the size of your file drawers - the bigger they are, the more files they can hold. Storage is generally supplied by a hard disk or hard drive (these mean the same thing). Today's computers have hard drives with capacities measured in the HUNDREDS of Gigabytes (GB) and some computers may even have a TERABYTE (1TB) or more (that's a TRILLION bytes) - sufficient space to store more than 10,000 songs! Modern hard drives are so large that the majority of clients I see are using less than half of the storage they have available.
So if you are concerned about running many programs at once - perhaps surfing the Web, editing a document and a spreadsheet, flipping through photos, playing music, etc. - then make sure you have plenty of memory or RAM. Upgrading your RAM is very inexpensive, whether you do it yourself or hire a professional to do so. But unless you have an enormous amount of music, photos, or especially videos, almost any modern computer is going to have plenty of storage for your needs.