What is sudo apt-get -f install?

See the manpage:

-f, --fix-broken
   Fix; attempt to correct a system with broken dependencies in place.
   This option, when used with install/remove, can omit any packages
   to permit APT to deduce a likely solution. If packages are
   specified, these have to completely correct the problem. The option
   is sometimes necessary when running APT for the first time; APT
   itself does not allow broken package dependencies to exist on a
   system. It is possible that a system's dependency structure can be
   so corrupt as to require manual intervention (which usually means
   using dselect(1) or dpkg --remove to eliminate some of the
   offending packages). Use of this option together with -m may
   produce an error in some situations. Configuration Item:
   APT::Get::Fix-Broken.

It's one of the first solutions when trying to solve umet dependencies. (See this question: How do I resolve unmet dependencies after adding a PPA?)