The .deb repository is built for Debian 6 and is architecture independent. Although built expressly for Debian 6, it can be installed on various ports such as amd64, i386, etc.
The repository does not work for Debian 7 because MySQL Utilities requires Python 2.6 and Debian 7 currently ships with Python 2.7. For Debian 7, use the source code repository to install MySQL Utilities.
After you download the file, install it using the following command or similar depending on your specific release or version of Debian:
sudo dpkg -i mysql-utilities-1.5.6-debian6.0_all.deb
MySQL Utilities requires Connector/Python to be installed. For additional information, see Section 1.1, “Prerequisites”.