The phrase "take after somebody" means to resemble or have similar characteristics as another person, often a family member. Here are some examples:
She takes after her mother in her love for cooking.
He takes after his grandfather's sense of humor.
You take after your aunt with your artistic talent.
In these examples, the speaker is saying that the person they are describing shares a particular trait or characteristic with someone else. This could be a physical trait, like eye color or hair texture, or a personality trait, like being outgoing or having a good sense of humor.
Sometimes, the phrase is also used to describe negative traits or behaviors. For example:
She takes after her father's stubbornness.
He takes after his uncle's bad temper.
In these cases, the speaker is saying that the person they are describing has inherited or learned a negative trait or behavior from someone else.