阶 (jiē): This character originally meant “stairs” or “steps.” Here, it signifies a rank, level, or echelon in society.
级 (jí): This character means “level” or “grade,” like in school (e.g., 年级 niánjí - grade level).
斗 (dòu): This character means “to fight,” “to struggle,” or “to contend.” It's a very active, confrontational word.
争 (zhēng): This character also means “to contend,” “to strive,” or “to vie for.”
The characters combine very literally. `阶级 (jiējí)` becomes “(social) class,” a person's level or rank in the social hierarchy. `斗争 (dòuzhēng)` is a powerful term for “struggle” or “fight.” Put together, `阶级斗争` is a direct and potent name for the concept of “class struggle.”