Pidió comes from the verbpedir (to ask for). In the past tense (preterite), -ir verbs that have an "e" in their stem often change that "e" to an "i", but only in the "he/she/it" and "they/you all" forms. So, él pidió (he asked) gets the change, but yo pedí (I asked) does not.
Why isn't there a word for "for" after pidió?
The verbpediralready means "to ask for" or "to request." You don't need to add a word like por or paraafter it. Él pidió covers the whole phrase "He asked for." (Note: to "ask a question," you would use a different verb, preguntar).
It can mean a turn in a game or a waiting line, but in many Latin American countries, un turno is also a very common way to say an "appointment" (like at the doctor) or a work "shift."