Learn Spanish (Latin America): Ella se parece a su madre.

You are right that parecer means to seem. However, adding the pronoun se changes the dictionary meaning of the verb. The pronominal verb parecerse means to physically look like or resemble someone.

Why do we need the word a after the verb?

The verb parecerse requires the preposition a to connect it to the person or thing being resembled. You can think of it as saying she looks similar to her mother.

Could I use como instead of a here, since it translates to like?

No, parecerse must always be followed by a, never como. If you want to use como, you would need a different verb structure entirely, such as ella es como su madre (she is like her mother).

Does se parece refer to physical appearance or personality?

In this context, it refers to physical resemblance. If you want to say she acts like her mother or has a similar personality, you would usually say ella es como su madre or use a verb about behavior.