"to sing out of tune" means to sing the wrong notes - either flat notes (lower than the true note) or sharp notes (higher than the true note). The antonym is "to sing in tune".
What is singing out of tune?
One, we may not be familiar with the notes or pitches that we are singing, or even the specific vocal range that the song is in. ... For example, a song may have a great number of pitch jumps, and we may not know how to sing these changes in pitch.
Why do I sound out of tune when I sing?
When you are out of tune, you are going to be either flat or sharp. This refers to which side of the musical pitch you are on – too low or too high. “Sharp” refers to being above the desired note; you are singing a little too high. When you are singing “flat,” it means you are a little below the note.