echo is a program used to show text. It can echo back what you type, or it can echo things such as environment variables ($HOME, $USER is an environment variable). Echo can also be used to pipe text to another program. For example:
echo hello world | wall
the | symbol is a pipe. In the most basic sense it is like saying "take the text hello world and send it to wall"
$HOME, $USER is a variable. It contains information. In order to access the contents of the variable you have to use the $ symbol.
If you wanted to, you can say just $HOME and then press enter, but you will be given an error, and that's not a very good idea either. Because without echo what you type on the shell will be interpreted as a command, or other things.... which I won't get into because I'll just confuse you even more.
So when you want to show text, you can use echo. If you want to send text to a file. You say echo "hello world" > my_file_name
Again, without using echo here, "hello world" will be interpreted as a command. The > symbol is used to redirect the text of "hello world" to a file.
You should also type 'man echo' without the quotes the next time you're in linux. The program 'man' will show you the manual of echo, the manuals can be a bit complicated to read, but you will get used to them. :)
A good beginners guide:
http://www.linux.org/lessons/beginner/index.html
good luck and have fun
EDIT:
Btw, you can type the command 'env' to show all of your environment variables. That is where $HOME and $USER is.
You should get a Live linux cd such as knoppix, you don't need to install it to your HD. It will run from your DVD/CD drive. The best way to learn linux is to use it, use it often, and read the man pages to find out what stuff does.