My mom had already cooked dinner before I got home.

had 是动词 have 的过去式，在这里表示"已经完成"的动作。 already 是副词，意思是"已经"，强调动作在某个时间点之前就已经完成。 had already cooked 构成过去完成时态，表示"在过去的某个时间点之前就已经完成了做饭这个动作"。