.bin is a binary executable, in other it's the equivalent of a .exe file in windows. usually, there is a symlink (symbolic link) to the .bin placed in the /bin or /sbin directory. in other words, say you're talking about Firefox. when you unpack the archive (.tgz), you'll notice a file called firefox inside the /firefox directory. if you type ls -l ./firefox/firefox you should see that it points to something.bin (i'm guessing here, i'm not actually sure firefox is configured this way). this means that if you are in this directory, you can type firefox and start the program. if you want to be able to run it from any directory, you need to add it to your PATH (the directories linux checks for commands) by doing this:
ln -s /path/to/firefox/firefox /bin/firefox
then anytime you type firefox (and anywhere) it will start the program. that's probably way more info than you wanted, but there you go.