Gems are packaging format used for distributing Ruby libraries. Think of it as a java jar file or a python egg. You can install/update these libraries by using the gem command, which will automatically download and install/update/build docs and the dependencies for the gem. It is similar in feel to using Debian's package manager "apt" to install software packages on linux.
Quite right. Note that another excellent advantage of RubyGems is that it's written in pure Ruby, so it runs anywhere Ruby runs. You can install some Ruby libraries with apt-get or Yum, but they are of course distribution specific. (They also typically lag behind the RubyGems distribution.)
Additionally, RubyGems offers versioning - you can request only a certain version of a gem, and you can have multiple versions of the same gem installed at once. This is a nice feature, and means that you can solve versioning issues with nice error messages instead of failing because of a missing method or class.