Troll Hives look similar to a giant gray beehive, and are filled with green jelly which has soft, tiny, white, glowing bubbles. This solution is kept at 150 degrees, presumably Fahrenheit, and reminds Sophie a little of Aloe Vera gel. They are used in Flashback to save Luna and Wynn's lives. Each compartment in the hive has a control panel with many buttons that can be used to close the compartment and fill it with the jelly, as Fitz and Biana discover after they lock Alvar in one.
These hives are necessary because troll babies are born at an incredibly early stage. They are then implanted into hives so they can finish developing and grow to a proper size. Trolls are also at their largest when they are young, so presumably they must be born before they are fully developed, or they would be too large for their mothers to bear.
Several thousand years before the books take place, the troll hives were raided by ogres. The trolls managed to fight them off and maintain control of their lands, but they lost an entire generation in the process.
To prevent this tragedy from repeating itself, Luzia Vacker helped them to hide their hives with illusions at Everglen near the lake. When more space was needed, they moved the hives to Dawnheath. A troll hive was discovered in Flashback to still be on the property of Everglen, covered by Luzia's illusions. The Trolls from the hive destroyed much of the property. Later in Flashback, it's revealed that Luzia had another hive hidden near the overdrive where she and Empress Pernille were secretly trying to design trolls that were both as smart and strong as newborns.
This Hive was kept secret until the the Celestial Festival when the Neverseen opened it. It was used by Empress Pernille and Luzia Vacker to try to illegally create Trolls that could be very strong and very smart at the same time. After the Neverseen opened it and exposed them, it was abandoned.
Hive Built for Alicorns
This was built after Luna and Wynn were born. The twins were born too early and needed somewhere to stay, so Sophie agreed to the alliance with the Trolls and they quickly built this hive in a tower. This hive was specifically built for Wynn and Luna and (presumably) has not been used since.