Apples will continue to ripen off the tree, but they have to get to a crucial stage first. The fruit's taste comes from many different compounds, but the key one is sugar (yes, even in tart apples). An unripe apple is full of starch, which doesn't taste very good. Over time, though, the apple starts to produce ethylene gas and triggers its own ripening process, whereby starch is converted into sugar. A fully ripe apple has replaced virtually all of its starch with sugar, but once that conversion is complete, the fruit also starts to go mushy. Incidentally, it's the same with bananas. A ripened banana tastes sweeter because it's completed its sugar conversion, whereas a green banana tastes bland and starchy. An unripe apple would be similarly bland, but no grocery store sells unripe apples.