Originates from baseball where a batter is out after missing three pitches. He missed the third job interview, it was like three strikes and you're out.
Pro Tip 2/3
Used Figuratively
Often used metaphorically for other situations with limited chances. I've broken my phone twice; three strikes and you're out, so I have to be careful.
Pro Tip 3/3
Not Always Literal
The number three isn't always literal; it suggests a limited number of tries. He was late to work many times; it was three strikes and you're out.