Robert Rouselle states in "The Journal of Psychohistory" that the Ancient Greeks believed in the veracity of dreams as portents of the gods and epiphanies that foreshadowed events of great import. Many cultures ascribe to the belief that dreams reveal metaphysical realities precluded by the physical limitations of the body. In fact, Greek writers employed even the dreams of women, (who were a mostly marginalized sex at best), to give weight to a particular theme or to catapault the plot, despite the fact that they didn't consider women's personal opinions any more than anecdotal. Perhaps writers felt the dreams of women were more trustworthy because of the embedded belief in the divine role of dreams.
According to Rouselle, "...whereas we would say 'I had a dream last night,' the ancient Greek would state 'I saw a dream last night.' Unlike most moderns, who believe that the dream comes from within, the Greeks considered themselves to be the passive recipient of the dream."
Hermes, messenger of the gods, comes to Odysseus in dreams to reveal divine messages. Athena consoles Penelope in dreams about her husband's absence in book four. However, as is the case with Prognosious and Calypso, dreams can be truths or glimpses of our most secretive desires, but can be twisted into deceit if the gods will them to be so.
Broadly speaking, the Greeks believed that there were two types of dreams. There are truthful dreams, which provide genuine omens and portents about the future. Then there are false dreams, which provide distractions that never come to pass. The false (or deceitful) dreams come through a gate of ivory, while the true dreams reach the dreamers through a gate made of horn.