These strange fruits (also known as sharon fruit) appear in Autumn and aren't so commonly seen in your average UK supermarket although their popularity appears to be on the increase.
Nutritionally, they have high levels of beta carotine, contain magnesium, calcium and iron, and are high in dietary fibre. Their phenolic compounds may well help combat heart disease too (think red wine).
To eat, allow the fruit to become jelly-like (think ripe kiwi) to reduce their astringent taste. You can cook them in dishes where you would use apple but they will lose their flavour somewhat.
If you fancy growing one, be patient. You need several to ensure good pollination and they will take probably 7 years or more before they fruit. They need good drainage and won't tolerate anything below -10c whilst they are establishing. As always, it's the damp, wet winters in the UK which will be their worst enemy.
On the plus side, they are considered highly ornamental and you can bet the neighbours won't have one!