Technically, afternoon starts at 12:01 pm, and continues until evening, which starts when it gets dark. Even if we say 'Good afternoon' more than the (virtually nonexistent) German equivalent, and use it in answering business telephone calls, in other contexts like greeting people face to face it's still not as common as just 'Hi' or 'Hello.'
I would say most people think of afternoon as the second half of the workday, that is, 1-5 pm. Noon to 1 pm is considered the lunch hour, when you can't necessarily expect people to be in the office or return calls. (Even if many of them only take a half hour, or eat something light at their desks.) If your lunch drags on until 2, or if you don't take it until after 1, people might consider it a late lunch. Not that that's uncommon, just that it's not necessarily the default.
I don't think most adults would plan to do something just 'this afternoon' or 'tomorrow afternoon' without setting a specific time. Or rather, you might tentatively settle on sometime in the afternoon and leave it at something like 'Why don't I call you when I'm leaving?' or '... when I know about what time I could come?'