Typically what you describe is referred to as spoofing, where the sender's e-mail address is faked.

As an example, think of the world e-mail system like the post office. This is effective, since the e-mail system was modeled after, well, the post office (hence e-mail being sent via the Post Office Protocol, or POP). When you send the letter, you will typically put the recipient's address in the center of the envelope, and your return address in the corner. The post office will then stamp the envelope with the town of origin, showing what post office originally handled the letter, and will also barcode the envelope.

In e-mail terms, the headers are like the envelope of a snail mail letter. Just like you can put any return address you want on a letter, you can put any return e-mail address on an e-mail you send. There are some defensive measures that are becoming prominent, such as the above mentioned SPF, but these measures are not yet commonplace.

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