Wordpress describes itself (http://wordpress.org/):
WordPress is a state-of-the-art publishing platform with a focus on aesthetics, web standards, and usability. WordPress is both free and priceless at the same time.
More simply, WordPress is what you use when you want to work with your blogging software, not fight it./
Coppermine describes itself (http://coppermine-gallery.net/) :
Coppermine is a multi-purpose fully-featured and integrated web picture gallery script written in PHP using GD or ImageMagick as image library with a MySQL backend.
Coppermine is free software which you can download and install on your webspace.
I use these commonly used and widely spread software systems and seeing them work together is awesome.
Note this article asumes that you are using Coppermine Galery System 1.44 and Wordpress 2.02. Currently there are newer versions of these software packages. Especially Wordpress offers a integrated Galery System nowadays but since i got tons of photos in my Coppermine galery and i dont want to integrate them in the new Wordpress version. I had to port the Coppermine Galery to work with Wordpress.
There is a plugin for Wordpress which helps you to integrate Coppermine photos in your posts (http://blog.artworkz.net/coppermineplugin/coppermine-4.5.1.tar.gz).
If you want to add the whole galery into your Wordpress blog you have to edit the theme of your wordpress blog.
I have provided a detailed step by step tutorial for this theme change on my own blog site (German language):
http://user.schule.at/home/?p=16