<img src="http://www.example.com/track.php?id=1">
In the mail to the second subscriber, you include this tag:
<img src="http://www.example.com/track.php?id=2">
And so on. There needs only be one file on your server to track opens no matter how many people you mailed: track.php.
That one file reads the "id" parameter from the request to know which subscriber opened the mail, and logs that in your database. It then creates a 1x1 transparent image, in memory, using GD, and outputs that to the browser that loaded the image tag.
The image never existed on disk, and nothing needed to be created in advance of sending a mail.
It may seem a little overkill, but I found doing it this way made a pretty significant impact when you have a reasonably decent volume of tracking going on. A good http server of course would cache the image of course, but we just found this to be easier and more consistent for our implementation.
dangrossman answered this in detail already and I agree with what he says.
Just as an example, in my system each email that gets sent out has a unique id (in our case a hashed id), we use that as the id value. From there we can get back to campaign, email address, company etc. As for the image itself, it is physically only one image generally (or an image byte stream cached in RAM).
btw -- dangrossman used sequential numbers as the ID only as an example to show you, you wouldn't do that in a production system. Have fun!