Can you provide a URL?
I was only able to find this version on sf.net: http://sourceforge.net/projects/reduce-algebra/files/reduce-x86_64-mac_10.6_snowleopard-darwin10.7.0-20110414.tar.bz2/download
That version is not a native Mac Cocoa app. And I do not know if there is a native Mac Cocoa app available. Cocoa is Mac's GUI interface/API.
To run that version you'll have to install X11. X11 may or may not be installed on your Mac. If not, you can get the install package from your OS/X installation media.
X11 is cross-platform client-server windowing technology. Thankfully it's included and supported by Apple. I use X11 everyday.
If that is the correct download URL, then launch X11 (Command-Space, then type X11 in spotlight and the X11 app should be a the top of the list if installed). When you launch X11 you'll be greeted with an xterm terminal window. From that window type:
cd ~/Downloads #or /Application if you dragged to Applications
tar jxvf reduce-x86_64-mac_10.6_snowleopard-darwin10.7.0-20110414.tar.bz2
#you may not need to execute "tar" if Safari automatically extracted for you.
#BTW you should turn off that "feature" of Safari for security reasons.
cd reduce-x86_64-mac_10.6_snowleopard-darwin10.7.0-20110414
./reduce
To make repeated invocations easier, then right click (or 2 finger tap) the X11 icon in the dock and select Options/Keep In Dock and then right click again and select Applications/Customize and add the above commands separated by semi-colons (e.g. cd ~/Downloads/reduce-x86_64-mac_10.6_snowleopard-darwin10.7.0-20110414; ./reduce). In the future you will just need to right-click on X11, then select Applications/Reduce.
I've never used this version of Reduce. I built my own from the source and run it from the CLI (xterm in my case).
Good luck.
Update, I forgot to add that you'll want to add the math fonts to your font path:
xset +fp $PWD/reduce.fonts/
This will make your X11 command line look like this assuming you extracted or moved the app to /Applications:
cd /Applications/reduce-x86_64-mac_10.6_snowleopard-darwin10.7.0-20110414; xset +fp $PWD/reduce.fonts/; ./reduce
Screen shot from my testing:
Edited: 20 May 2011, 9:20 a.m.