Computers have many different types of memory. The concepts are not as hard as people think. This is a mile-high fly-over of what the different types of memory are, and what they are used for.
There are a few types of memory in your computer. These generally fall into the categories of either temporary storage (only while the power is on), or permanent storage (remembers everything even when the power is off). Your hard-drives and CD-ROMs are permanent storage, it is where you save things when the power is going to turn off, but they are not technically called "memory". Memory is electronic chips that are inside of your computer, not mechanical devices (like hard drives or CD-ROM's).
HOW MEMORY IS COUNTED
Memory is just a collection of 1's and 0's called "bits". Similar to counting on your fingers (which are either up or down) this is probably where the term "digital" came from. When they are grouped together, you can count to very large numbers, or represent all the characters in the alphabet (if you used unique finger patterns to represent each character). Computer memory has a lot of these bits (digits).
Bits are grouped by 8's- called Bytes. Each Byte contains a value between 0 and 255, or is used to represent some character of the alphabet (or digit or symbol, etc.). By grouping bytes you can make very large numbers, or pages of characters (words, sentences, paragraphs, etc.).
Bytes are further grouped into kilobytes or "K" which is not 1,000 bytes, but close. The grouping goes on to million (Megabytes), billion (Gigabytes), trillion (Terabytes), quadrillion (Petabytes), and so on.
People usually think in base 10 -- 10's, 100's, 1,000's and so on. So we used those groupings to make the computer groupings. However, the computer deals in powers of 2 (not 10). So the number closest to 1,000 that is a power of 2, is 1024 (2 to the power of 10). Many people round 1024 to 1,000 and call that 1K, but this "rounding error" causes for errors and confusion. Look at the following table on what happens.
So remember that 1K in computer-speak is 1,024 and is not 1,000.
How much space does something take?
Important to users is not the name, but what that memory space could (or does) represent. Many people need a frame of reference for what a bit, byte or megabyte can store. Numbers and text are pretty space efficient in computers; but Sound, pictures, video, may not be.
Because some things are space efficient and other are not, programmers had to come up with tricks (compression) that allow them to pack more data into the same amount of space (by using some complex math). Random data you can often compress to 1/2 of the original size (average), sound can be compressed to 1/4 the original size, pictures can be made 1/40th the original size, and movies/video can be compressed to 1/400th the original size. The following table will give you an idea of how much space things take to represent in their raw (uncompressed) form -- but compressed data can be much more efficient.
For now memory (RAM and ROM) is usually measured in Megabytes (or occasionally Kilobytes), and most hard-drives are measured in Gigabytes. But progress marches on, and in a few more years we could have Gigabytes of RAM, and Terabytes of hard-drive space.
To understand about the types of memory --
I believe this set of articles will give you a very good understanding of the basic kinds of memory, and how they vary. Describing some complex concepts in a paragraph is likely to require some "glossing over". However, if you can read and understand this article, then you will have a good knowledge foundation and you can further explore the concepts in much more detail... if you want to (though it will not be necessary for most people). If you didn't get it all, don't worry, there are Hardware engineers who don't know all this stuff, and who don't need to. I do hope this article satiates any curiosity about memory issues that you may have.