English verbs don't really express futurity - they see everything from the point of the present. The continous expresses a temporary, on-going event. On going means that it's started but not yet finished ( ie it's in progress), while temporary means that the end is foreseen. So :
Peter is eating his dinner - he's already started, the action is on-going, but it's obvious that he'll finish in ten minutes or so (OK, Michèle - three hours or so if you're in France
)
The odd thing is that English grammar considers an event to have started as soon as it is arranged. So :
I'm meeting David next Monday - we arranged to meet last Friday (the start of the action) and on Monday when we meet, the action finishes. So I'm now in the middle of it - just as Peter was in the middle of his dinner.
This is reflected in the usual explanation that the continous expresses "future arrangements". But actually, the arrangements are past. It's the event which is future, and we're at a point somewheere between the start and finish. Other examples :
I'm flying to New York on Oct. 5th - ie I bought the tickets last week (start of the event), it's now late september (in the middle) and go to New York tomorrow (end of the event)
I'm working late on Friday - Yesterday I agreed to work late (start of the event) it's now Wednesday (mid point) and Friday evening will find me slaving in the office (end point)