Preferences
TeX Live Utility has very few preferences, in order to keep things as simple as possible. However, a few global options can be set in the panel available via the Preferences item of the main menu:
TeX programs
This is the path to the tlmgr command-line tool that TeX Live Utility uses. For Mac OS X 10.11 and later, the correct path is /Library/TeX/texbin if you have MacTeX 2015 or later; if you have an earlier version of MacTeX on OS X 10.11, the note below on the standard UNIX installer applies. If you use MacTeX 2014 and earlier on Mac OS X 10.10 and earlier, the setting of /usr/texbin is correct.
Note: /Library will be translated if you use a non-English language setting for your operating system, even if TeX Live Utility is not translated into your language.
For TeX Live 2014 installed via the standard UNIX installer with default options, /usr/local/texlive/2014/bin/x86_64-darwin would be the correct path. You may have to type / (a single forward slash keystroke) when presented with the open panel, in order to navigate to this directory, since it's hidden.
Other distributions require you to change this using the Choose… button or by dropping a folder on the path control to the left of the button.
Automatically enable fonts in my home directory
When checked, TeX Live Utility's will run the updmap command if it finds an updmap.cfg file in your TeX Live home directory, indicating that you have installed some personal fonts. If you have not manually installed fonts, as discussed here, you can leave this unchecked. Note: this setting only applies to TeX Live 2012 and later.
Show progress in system log
When checked, TeX Live Utility's log output will be written to the system log. Now that logs are saved between sessions, this should generally be left unchecked.
Add new packages to match the server when updating
If packages were added to TeX Live after you installed it, this will bring you up to date. You should almost never uncheck this box.
Remove packages to match the server when updating.
Sometimes packages are removed from the server, typically due to licensing problems. If this box is checked, such packages will be removed from your system when you use the Update All action.
This box can generally be unchecked safely, if you're concerned about losing packages.
List fonts can be changed by using the standard Font panel from the Edit menu (Cmd-T). Font settings will persist between launches.