Coming out of left field means that something is odd, unusual, unexpected or inexplicable. Something that slaps you upside the head and surprises you.
Parent: "I see you've been accepted to both Harvard and Yale. Which school have you decided to attend?"
Son: "I've decided that I'm going to spend the next year hiking across Turkey."
Parent: "What?! Well, that news certainly came out of left field."
"Left field" is a reference to baseball, although the actual origin of the phrase is in dispute. Many believe that it refers to early ballparks, where left field was often larger than right field and therefore was home to more lost balls and general confusion.
Student or Learner