A single line or single stretch/strand — e.g., a beam of light, a stretch of road, a strand of hair; one continuous length.
朝の光が窓から一筋差し込んだ。
A shaft of morning light streamed through the window.
道に沿って一筋の並木が続いている。
A single row of trees continues along the road.
彼の髪には白い一筋が入っていた。
There was a white streak in his hair.
Earnest, single-minded, or resolute — devoted to one thing without wavering; often used as a suffix to describe devotion or focus.
彼は仕事に一筋で、休日も勉強している。
He is single-minded about his work and studies even on his days off.
恋に一筋な姿勢は尊敬されるが、時には柔軟さも必要だ。
Being devoted in love is admirable, but sometimes flexibility is also necessary.
Archaic usage referring to a single bloodline or clan; rarely used in modern Japanese.
（文語）彼は一筋の名門の出であると伝えられている。
It is said (in literary style) that he comes from a single noble lineage.
Archaic meaning 'ordinary' or 'common'; seldom used nowadays.
（文語）その考えは当時一筋であったと記されている。
It is recorded (in literary style) that that idea was ordinary/common at the time.