Whenever you see a word starting with "mega-," it usually means there is 1,000,000 (a million) of something, though sometimes people just use it to mean "really big!"
To talk about this "mega" computer word, we have to start with something very small: the bit. The word bit has a few meanings, but in computers, it means something special. It is a small piece of computer information that can tell a computer "yes" or "no." The word bit is contracted from the words "binary digit." If you take out most of those middle letters, you'll get "bit." A binary digit is a 1 or a 0, and those two numbers can tell a computer a lot! Yes or No. True or False. On or off.
Now for a little math: Eight bits make up a byte. And about one million bytes make up a megabyte. We use megabyte to talk about the sizes of computer files. If a computer program takes 50 megabytes to run, we have to make sure there are 50 megabytes of empty space on our computers so the program will fit. Since we can't measure a computer program or file in feet or inches, we need special measurements. That's why we use bytes, megabytes, and other "byte" words like kilobyte and gigabyte.
To get a sense of size, a minute of music that you put on an iPod (an MP3 file) is about 1 megabyte in size.
You know now the mega means a million. There are many other prefixes, or parts of words added to the beginnings of other words, that mean different numbers. Kilo is a common one. It means one thousand. A kilobyte is 1000 bytes. A kilometer is 1000 meters. Giga means one billion, so we have gigabytes. Hecto means 100, and deca means ten (10.) Those two are less common.
Where do you see these and other prefixes in the world around you? Many words have numbers built right into their names! Think about centimeters, decathlons, bicentennials, centipedes, millipedes, and centuries. What are the number parts of those words? What do they mean?
The size of a megabyte isn't always consistent (the same). In the past, megabytes have had different sizes. These sizes are still being used today, and they are still called megabytes. This will probably never be an issue unless you are really into computers, but for those of you who are or might be, be on the lookout for these other megabyte sizes.
A megabyte can be 1,000,000 bytes, 1,048,576 bytes, or sometimes 1,024,000 bytes. But don't worry about those numbers until you go to college for a computer science degree.