卡壳 is a separable verb (离合词) that originally described a gun jamming — a cartridge getting stuck in the chamber. Today it's used broadly for any situation where things get stuck or stall, especially in speaking, thinking, or processes. The verb-object structure (卡 + 壳) allows insertions like 了, complements, or duration between the two syllables: 卡了壳, 卡住壳, 卡过壳.