I found this online:
Keep in mind these are used differently in Latin America and Spain. In Spain, the tendency is to use afuera with motion verbs, the same way that adonde is used, and to use fuera with state verbs. Estoy fuera (I'm outside), voy afuera (I'm going outside). But in Latin America, afuera is used for both.
'Espero' is the 1st person conjugation of the verb 'esperar'. It specifically means 'I wait' OR 'I am waiting'. It can be translated to both because English can use either form for present tense events.
In contrast, 'esperando' is the verb in its gerundio form. It is used in the present progressive tense only. That tense is used to emphasize that the action is currently happening (as Duo's sentence here). The present progressive tense must use the verb 'estar'. So 'Estoy' (I am) 'esperando' (waiting). Did that help?