Dryads appear to have a tertiary stage of sexual development focused on their becoming receptively fertile. The stage is evidently linked to them psychically bonding with a particular sort of tree (a great oak) found in their homeland, the Woods of the North. The dryads form a close bond with this planted tree and its well-being becomes an analogue of their own well-being.
There's a fleeting reference to this earlier in the Guardians of the West:
"She's only nineteen, Brand."
"Most Alorn girls have had at least two babies by the time they're
"Ce'Nedra isn't an Alorn. She's not even entirely Tolnedran. Her
heritage is Dryad, and there are some peculiarities about Dryads and
the way they mature."Guardian of the West
and a fair amount of additional detail in the sequel; King of the Murgos.
"Ce'Nedra's background makes her peculiarly sensitive to trees,"
Polgara explained. "I didn't know that Tolnedrans were that interested
in the out-of-doors." "She's only half Tolnedran, Liselle. Her love of
trees comes from the other side of her heritage." "I'm a Dryad,"
Ce'Nedra said simply, her eyes still dreamy. - "I didn't know that."
"We didn't exactly make an issue of it," Belgarath told her. "We were
having trouble enough getting the Alorns to accept a Tolnedran as the
Rivan Queen without complicating matters by telling them that she was
a nonhuman as well." - King of the Murgos
Due to the psychic connection, when the tree is young and frisky, the dryad is frisky. When the tree sheds in winter, the dryad becomes saddened and when the tree nears the end of its life, the dryad becomes tired and depressed.
"Are you unwell, Xantha?" Polgara asked her. The queen sighed. "The
time is growing close, that's all." She looked up affectionately at
her enormous oak. "He's growing very tired, and his weight presses
down upon his roots. He finds it harder and harder each spring to
revive himself and put forth leaves." "Can I do anything?" "No,
dearest Polgara. There's no pain — just a great weariness. I won't
mind sleeping. Now, what brings you into our Wood?" King of
Ce'Nedra's oak tree wasn't thriving (in the harsh soil, because of the accidental ice age that Garion had nearly triggered and because it was suffering (psychically) from the argument between her and Garion) and as a result, she hadn't entered a fertile phase.
By re-planting the tree in loam that had been psychically charged with the couple's sexual enegies (hence why the supplies needed to be near the marriage bed) and by having her drink a tonic made from the oak's own buds, Polgara was able to convince Ce'Nedra's body that it was time to breed.