An 'entertaining' sentence could depend upon mood. At the grave side, "We will remember him." And call me unfeeling, but in the definition of 'entertain' can be found the word 'divert' as well as the word 'amuse.' 'Entertain' can also imply some part of the words 'think about.' For example, "At least entertain the idea of liberal democracy." Of course it's possible to totally isolate the noun 'entertainment,' put it down as a product which might be called, 'what it is a person entitles himself to when the chores are done.' But, I wouldn't be me if I thought that, so better to think of the word 'entertain' and its products, as belonging to sets of words that have in their meaning, 'engage the attention of another.'
Then to the question, 'why entertain?' The answer can be 'for money' or for a whole range of other consequences that might flow to the 'entertainer' as a result of 'engaging the attention of another.' And for some reason I find it 'entertaining' that in the history of the word 'entertain,' there was a time when 'entertain' had the word 'hire' in it's meaning. A powerful person, would 'entertain' the services of a less powerful person. And a long road it has been, so we should 'entertain' few illusions about the distinction we draw between 'entertain' and 'hire'. And why does a creepy, pedantic old fart, even mention these matters. Probably better just to think of it as the sort of random and dissociative heckling one expects from a grandparent.