The world on which the spiders live has been created by terraforming carried out by humans from Earth, and is one of a number of similar projects undertaken in the remote past by the 'Old Empire'. But civil war led to the destruction of that civilisation, and Dr Avrana Kern, the scientist in charge of the spiders' world, had been left on her own for millennia. (Individuals can live for centuries in a form of artificial hibernation, although by this time she has largely uploaded herself into a computer to ensure the survival of her monitoring capacity.)
The spiders' spectacular evolutionary advance came about by accident. Kern's plan had been to place monkeys on the planet and infect them with a virus that would accelerate their evolution dramatically. But things went wrong and the monkeys were destroyed en route to the planet; the virus instead infected the spiders and produced its evolutionary acceleration in them, although Kern doesn't know this.
Meanwhile a new civilisation has developed on Earth in the ruins of the old. It is not as technologically advanced as the Old Empire and is parasitic on what is left of its technology, including its space stations. The Earth has not recovered from the devastating war that ended the Old Empire and in fact is about to become uninhabitable, so the plan is to send out spaceships carrying thousands of emigrants in the desperate hope that at least one will find a terraformed planet and so ensure the survival of humans. One of these spaceships, the Gilgamesh, has found Kern's world and wants to settle there, but it encounters fierce resistance from Kern. If they are not allowed to land and settle it will probably be the end of humanity.
Most of the book is composed of alternating chapters, in which we see events through the eyes of individual spiders or, in the human world, through those of Holsten Mason, a historian or 'Classicist' whose responsibility it is to interpret communications and records written in the language of the Old Empire. Mason is in hibernation for much of the time but is woken up periodically when his services are required.
This is an ambitious book but I should say it largely succeeds in what it sets out to do. The characters, both human and arachnid, are three-dimensional and convincing; you do care what happens to them—even arachnophobes will probably find themselves emotionally involved. But what really distinguishes this book is the detailed account of how the spiders develop a technology based on the physical and mental resources available to them, using remarkable but not impossible inventiveness and adaptability.
In this respect the choice of Portia labiata was a good one. The real Portia is an astonishingly intelligent creature that hunts other spiders often bigger than itself and makes flexible plans, requiring foresight, for its attacks. This foresight continues to characterise the species throughout its evolution in the novel.
Some science fiction has elements of allegory, and I think that is true here. Spider and human society are alike in some ways but quite different in others; among the spiders females are completely dominant and the fatal human propensity to civil strife is lacking. To my surprise, by the end I found myself reminded of the episode in Gulliver's Travels in which Gulliver arrives in the land of the Houyhnhms. We could see the spiders in the role of the virtuous Houyhnhms and the humans on the Gilgamesh as the appalling Yahoos. But the contrast is not as stark as it is in Gulliver and, at the end, the humans are redeemed.