There are some terms used throughout the game in Spira that can be confusing to a player. Heck, they were confusing to Tidus. Here is a small dictionary to help you better understand Spira.
Aeon - Powerful beasts that can be summoned to fight for a summoner. They are dreams of the fayth. The aeons available in the game are Valefor, Ifrit, Shiva, Ixion, Bahamut, Anima, Yojimbo, and the three Magus Sisters.
Blitzball - A popular sport in Spira. It's played in a sphere of water, and is much like soccer.
Calm - The ten-year period of peace after a summoner defeats Sin, before it appears again.
Crusaders - An organization of volunteer warriors who defend the people of Spira against Sin.
The Farplane - A place where the dead go after they are sent. The people of Spira visit the Farplane to talk to loved ones. Memories of their loved ones are materialized before them.
Fayth - Humans who willingly gave up their lives to have their souls sealed in statues summoners pray to. They can be recruited as aeons.
Grand Maester - The senior leader of Yevon. The only position higher than Maester.
Machina - Machines. Most often, machina refers to robot fiends and weapons. They are strictly forbidden by Yevon.
Maester - A leader of Yevon. There are three Maester positions: one held by a human, one held by a Guado, and one held by a Ronso.
Sending - When someone dies in Spira, a summoner sends their souls to the Farplane. This act is called a sending. If a soul is not sent, it becomes a fiend, stuck in the world, angry and jealous of the living.
Yevon - Spira's organized religion. Tidus and the party discover Yevon is not completely what it seems.