A paean is a hymn of praise or thanksgiving. You might sing a paean in church, where many hymns extol the greatness of God.
Paean was originally a song of praise for Apollo, or Paian as he was sometimes called. You can now use paean to mean any song of praise, regardless of the deity, or to mean a formal expression of praise, like a eulogy. At your mother's birthday dinner, it might be nice for you and your brothers and sisters to write and sing a paean to her good-natured love and support of you over many years.