I could just say, "that's why it's called a mystery" and leave it there, but I won't. The Eleusinian Mysteries were the most widespread of the mystery religions and they were biggest in Eleusis (that's a place in Greece). They were very focused on Demeter and Persephone.
a herm was a boundary stone or pillar, often with the head of Hermes, Dionysus or Heracles on top and his protruding somewhere lower - male genitalia was believed to be an affective protection from evil;
In psychoanalysis, a subconcious sexual desire in a child, especially a male child, for the parent of the opposite sex, usually accompanied by hostility to the parent of the same sex. If unresolved naturally, this complex may result in neurosis and an inability to form normal sexual relationships in adulthood.
~The American Heritage Dictionary~
This comes from the story of Oedipus.
The mountain where a bunch of the real big Classical gods lived, like Zeus and Hera and Athena and lots of other major gods (but not Poseidon or Hades) lived. There is an actual Mt. Olympus, and a place called Olympus, but this is a more mythical Olympus.
the conception and creation of offspring with only one parent. For instance, in some version's of Hephaestus' birth, Hera was the parthenogenic mother of Hephaestus; comes from the greek roots: "parthenos" or virgin and "genesis" or birth;
essentially a family system, culture, society, etc. where father figures rule. Zeus, the Father, rules the gods. Ancient Greece was a patriarchal society and women were often relatively powerless because of this.
The Underworld is where people go when they die. There is a tradition of putting gold coins on dead people to pay the ferryman to cross the river. It's sometimes called Hades - intended to refer to the place OF Hades - and people sometimes forget that he's the god, not the place. Persephone rules with Hades.