In my great-grandmother's recipe for Open-Face Apple Pie, she writes, "Cut apples in eighths if they are not quick-cooking." I assume that this means some apples will cook more quickly than others, but I can't find a list of such apples anywhere.
One of my favorite topics, having grown up close to two apple orchards...
Most likely, by "quick-cooking," the recipe intends you to use a pie or sauce apple, i.e. one that softens readily with heat.
Which apple to use is certainly a matter of preference. Some people like their pie apples to remain quite firm (using, say, Granny Smith), while others like them to be VERY soft (and thus use a "sauce" apple).
Here's some apple lists/charts ... I'd say look up the varieties readily available to you, and see which ones are listed for sauces or pies.
Look up the website for your local orchard - they may link to a usage chart for the apples they grow!
This might relate to the 'hardness' of the apples. Some apples cook down to a sauce much quicker than others (Bramely might be considered quick cooking whilst Cox's might be considered slow cooking).