The afternoon is the part of each day that begins at noon or lunchtime and ends at about six o'clock, or after it is dark in winter.
the present day
You refer to the afternoon of the present day as this afternoon.
I rang Pat this afternoon.
Can I see you this afternoon?
You refer to the afternoon of the previous day as yesterday afternoon.
Doctors operated on the injury yesterday afternoon.
You refer to the afternoon of the next day as tomorrow afternoon.
I'll be home tomorrow afternoon.
single events in the past
If you want to say that something happened during a particular afternoon in the past, you use on.
Olivia was due to arrive on Friday afternoon.
The box was delivered on the afternoon before my departure.
If you have been describing what happened during a particular day, you can then say that something happened that afternoon or in the afternoon.
That afternoon I phoned Bill.
I left Walsall in the afternoon and went by bus to Nottingham.
If you are talking about a day in the past and you want to mention that something had happened during the afternoon of the day before, you say that it had happened the previous afternoon.
He had spoken to me the previous afternoon.
If you want to say that something happened during the afternoon of the next day, you say that it happened the following afternoon.
I arrived at the village the following afternoon.
talking about the future
If you want to say that something will happen during a particular afternoon in the future, you use on.
The meeting will be on Wednesday afternoon.
If you are already talking about a day in the future, you can say that something will happen in the afternoon.
We will arrive at Pisa early in the morning, then in the afternoon we will go on to Florence.
If you are talking about a day in the future and you want to say that something will happen during the afternoon of the next day, you say that it will happen the following afternoon.
You leave on Thursday, arriving in Cairo at 9.45pm, then fly on to Luxor the following afternoon.
If something happens or happened regularly every afternoon, you say that it happens or happened in the afternoon or in the afternoons.
He is usually busy in the afternoons.
In the afternoon he would take a nap.
If you want to say that something happens regularly once a week during a particular afternoon, you use on followed by the name of a day of the week and afternoons.
She plays tennis on Saturday afternoons.
In informal English, you can use afternoons without ‘on’ or ‘in’.
She worked afternoons at her parents' shop.
If you have mentioned an exact time and you want to make it clear that you are talking about the afternoon rather than the early morning, you add in the afternoon.
We arrived at three in the afternoon.