A wedding is a ceremony that in some form or another has been independently created on many humanoid homeworlds. It is the act of marrying two or more people depending on culture often for the purpose of religion and/or sexual reproduction.
Weddings in the Federation are usually performed by Federation or Starfleet officials. Jean-Luc Picard married Miles O'Brien and Keiko Ishikawa in 2367. William Ross performed Benjamin Sisko and Kasidy Yates' wedding in 2375. Katherine Janeway married Tom Paris and B'Elanna Torres (as did their demon planet mnemetic copies). (TNG: "Data's Day", DS9: "Til Death Do Us Part", VOY: "Course: Oblivion", "Drive")