Always paired conceptually with 主线 (zhǔxiàn, main line / main storyline). Common in three domains: transportation (支线铁路, 支线航班), narrative (支线剧情, 支线任务 — used heavily in video game discussion), and electrical/network topology.
memory
支 (branch) + 线 (line) = a line that branches off the main one. 支 also gives 支流 (tributary) and 分支 (branch / fork).