A singer-songwriter is a person who writes songs and then sings them. There's more to it than that, however: the "singer-songwriter" label is associated with certain styles of music. Traditionally, the label refers to Three Chords and the Truth music in which a single singer accompanies themself with only an acoustic guitar or a piano, but you'll also find singer-songwriters in pop and rock. The defining characteristics of a singer-songwriter is that they are billed individually rather than as part of a band, that they write their own songs, and that the emphasis is on the lyrics rather than on complex music (this is why you don't call Jimi Hendrix or Frank Zappa "singer-songwriters", even though they did sing and write songs). Singer-songwriter music was especially popular in The '70s.

Notable singer-songwriters include:

Australia

Belgium

Jacques Brel
Raymond Van Het Groenewoud

Britain

Canada

Yoko Ono
Toshiyuki Toyonaga - yes, the voice actor. In addition to that - and singing in about five different boy band anime - he also does this style of music. He wrote and performed the second opening of Durarara X2, "Day You Laugh", and he wrote the song that the singer character in the show performs, as well.
Utada Hikaru

The Netherlands