Learn Spanish (Latin America): La chica afirmó que el jefe buscaba al empleado. - The girl stated that the boss was looking for the employee.

This sentence uses reported speech. The reporting verb afirmó is in the past. If we heard the girl's original direct words, she would have used the present tense: el jefe busca al empleado. When we report a present-tense statement using a past-tense reporting verb, the reported verb shifts to the imperfect tense, becoming buscaba.

Could we use dijo instead of afirmó in this sentence?

Absolutely. Afirmó comes from afirmar, meaning "to state" or "to declare", which is just a slightly more formal way to report speech. If you used dijo (said), it would trigger the exact same tense shift to buscaba in the second half of the sentence.

Why isn't there a Spanish word for "for" after buscaba?

The verb buscar already means "to look for" or "to search for". English splits this idea into a verb and a preposition, but Spanish builds it all into the single verb. Adding por or para after buscaba would be incorrect here.

Why does the sentence use al empleado instead of just el empleado?