Literally: self – picture – self – praise
Alternately: Singing one’s own praises. Blowing one’s own horn. (Public) self-congratulation.
Note: Although the 賛 can be translated as “praise,” in this case it refers to a tradition of writing poetry, or something of a similar literary bent, in response to (and perhaps to accompany) a picture. Such a written piece is also called 賛. So while the meaning is unchanged, 自画自賛 refers to ‘writing a poem in response to one’s own painting’ rather than directly, overtly praising one’s own work. Perhaps this distinction gives us a little window into traditional Japanese culture.