My host father is crazy about these things. And I will say as much as I don't dislike them either. It goes under the names Sugar-Apple and sweetsop and in Taiwan it's also known as Buddhas Head Melon, as it resembles the head of the Gautama Buddha.
They're some little Taiwanese that, according to one of my readers, probably originated from South America. Thanks goes to Carlos. He seems to have referred to the Cherimoya, which is not exactly this fruit as far as pictures from the web tell me, but I could imagine that they still have something in common about origin.
I believe there are a few little details that makes the Taiwanese Sugar-Apple slightly different from other countries sugar-apples. A more important thing is, however, that you don't mix it up with other fruits in the Annona family such as Soursop, Cherimoya, Custard-Apple or Atemoya, (which is a hybrid between Cherimoya and Sugar-Apple.)
In the picture above, you see that it is possible to rip the peel off of the fruit without much effort should your fruit be mature and soft. Don't eat it while it's hard, wait a while instead, and it will taste better.
Allow me to cite Wikipedia for a suiting description of the meat:
The fruit flesh is sweet, white to light yellow, and resembles and tastes like custard. The edible portion coats the seeds generously; a bit like the gooey portion of a tomato seed. Sugar-apple has a very distinct, sweet-smelling fragrance. The texture of the flesh that coats the seeds is a bit like the center of a very ripe guava (excluding the seeds). It is slightly grainy, a bit slippery, very sweet and very soft. The seeds are scattered through the fruit flesh; the seed coats are blackish-brown, 12–18 mm (0.47–0.71 in) long, and hard and shiny. - Wikipedia on the Sugar Apple
You'll usually pick out the little chunks of meat with a spoon as they are covered in sticky fruit juice. One thing you can also see on this picture is a bit of the contents that Wikipedia forgets completely about. There's also some substance with a much different texture and taste yet still creamy and sweet in between the clusters of meat and the peel of the fruit - possibly as a protective buffer. It can also be eaten and although it's not the major part of the fruit, you can still eat a bit of it, especially if you scrape the peel from the inside lightly. Look at the picture above and you can see some of it running down the side of the fruit almost in the middle of the picture.
There's still a lot left for me here, so I'll get back to you another day. If you get the chance some day, try it!