This term (the German word for song) refers to songs for solo voice, accompanied by piano. This is a style which emerged during the Romantic Period and was pioneered by Schubert who wrote over 600 songs in this style. Other composers include Beethoven, Schumann and Liszt.
An interesting feature of Lieder is that the voice and piano are equally important – both the voice and the piano having opportunities to be showcased and where the writing for each is intertwined.
'An Die Musik' by Schubert is an example of a Lied is in Strophic form (i.e. the same music is used for each verse). It is sung by a Baritone.
'Erlkönig' (again by Schubert) is an example of a Lied which is through-composed (there is no repeat of sections). This song is a story involving different characters (narrator, father, son and Erlkönig). At different times in the performance, the singer changes his body language and tone of voice to portray the different characters.
BBC: Definition of Lieder
This link to the BBC Bitesize website gives an opportunity to explore Lieder more fully.
'An Die Musik' by Schubert is an example of a Lied in strophic form.
Ian Bostridge sings 'Erlkönig'.