Harvest is just the beginning so far as your squash are concerned. If you take one in the house and cook it you will probably be very disappointed. When the plant quits delivering nutrients to the squash it takes on a life of its own and starts preparing itself for the next step, replanting the next generation of squash.
What that means is that the seeds continue to ripen for some time, absorbing nutrients from the “meat” of the squash, and at the same time the flesh starts converting stored carbohydrates into sugars to make the nutrients more accessible. Some of the water is also absorbed, making the flesh firmer and drier.
From our point of view, as time goes on the flesh gets drier, firmer and sweeter. This process occurs at different rates in different varieties of squash. The C.pepo squash, such as acorns and delicatas cure quickly. Give them a couple of weeks after harvest and they’ll be great. You can recognize them by the small stems usually with flattish sides and often sharp corners.
On the other hand, C. maxima varieties such as Hubbards, sweetmeats and other larger squash can take months to really cure and reach their best eating. C. maxima squash have big round “corky” stems and true to their name are often large squash.
I understand that traditionally people would wait until Thanksgiving to open their first big squash. It can be awfully hard to wait that long if don’t have a lot of small squash to get you through, but do try to put it off as long as possible and you’ll be rewarded with better tasting squash. A well-grown and well-cured squash is hard to beat for delicious food, it’s always a sad day when the last delicata is gone but at least I’ve still got the big guys for the rest of the winter.