Refers to one's family line or descent. Somewhat formal or literary; in everyday speech, 家系 (かけい) or 血筋 (ちすじ) are more common.
彼は由緒ある筋縄の出だ。
He comes from a distinguished lineage.
Compound of 筋 (すじ, 'line, thread') and 縄 (なわ, 'rope'), metaphorically referring to a connected line of descent. The exact historical derivation is uncertain.