Literally: true – one – sentence – character
Alternately: Straight as an arrow; as the crow flies; as straight as the written character for the number one, which is just a straight line. By extension; when a person’s actions are focused, single-minded.
Notes: Keep in mind that 文 here is not adding significant meaning on its own; 文字 (usually pronounced moji in contemporary Japanese) refers to a written or printed character. If we divide up the parts of this yojijukugo, it’s not half-and-half but 真 modifying 一文字 “the character for ‘one’.”
There’s a set phrase for compressing your mouth into a straight line: 真一文字に口を結ぶ (maichi monji ni kuchi wo musubu).