Most of your installed software (not including Subsonic) is provided by configured software sources (also called repositories) from which software is automatically downloaded and installed by the package manager. Running these commands will upgrade all such software to the latest versions provided in your configured software sources:
sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade
See the apt-get manpage for explanation of specifically what those commands do. (Also accessible on your machine via man apt-get.)
However, Subsonic was not installed in this way. Following these instructions, you manually downloaded the installer package (.deb file) for Subsonic, and installed it by manually invoking the dpkg command with the -i flag. Unlike most software for Ubuntu, Subsonic doesn't have a software source you can set up to provide it, so that's the way you have to install it. To upgrade it to a later version, simply download the newest .deb file (or whatever version you want to upgrade to) and follow those same installation instructions (with the new .deb file).
Since Subsonic is not automatically upgraded with the rest of the software on your system (via apt-get), you'll have to take care to remain current on issues that affect it so that you know when security vulnerabilities are discovered and when they are patched (i.e., when a new version is released to fix the vulnerability). In practice, all network server software of greater than an extremely minimal degree of complexity has multiple security vulnerabilities, which are discovered (and hopefully also fixed) from time to time.
Sometime in the future, you may have the preferable alternative of using a non-official software source (of a kind called a PPA) for Subsonic. You would then receive updates to Subsonic along with updates to the rest of the software on your system (via apt-get). However, currently the Subsonic PPA is empty and does not provide any software.
