Moon - roughly a month. On this site, a moon is a week.
Anyone who has read the Warriors Series by Erin Hunter is familiar with the Clan and Tribe rankings.
Kit - a cat under 6 moons of age. (See above) A kit cannot become an apprentice until it is atleast six moons old.
Apprentice - a cat over 6 moons of age. An apprentice cannot become a warrior until it is at least 12 moons old. The exact amount of time is chosen by the apprentice's mentor and the Clan's leader.
Warrior - a warrior must be over 12 moons of age. It must know how to hunt, fight and defend it's Clan.
Elder - a warrior has the option to decide when and if to retire. They are generally over 20 moons old, but may retire early if has reasons. The leader cannot make a warrior an elder without the warrior's consent.
Queen - a queen must be at least 14 moons old. The same goes for toms - no cat under 14 moons may have a mate.
Deputy - as specified in the Warrior Code, a cat cannot become deputy if he or she has not had at least one apprentice. After the death of a deputy, a new one must be named before moonhigh.
Same as Clan; a queen is a kit-mother, and an elder is, of course, and elder. An apprentice is a to-be, and prey-hunters and cave-guards are warriors.
Tigerstar - A Tigerstar is a user who is extremely rude and cruel, particularly to their own Clanmates.
Brokenstar - A leader who, as specified above, makes a kit an apprentice too early, a apprentice a warrior, and so on.
Hawkfrost - A user who makes their Clanmates do things they don't want to.
Crowfeather - A user who switches mates much too often.
Squirrelflight - A user who has an extremely bad habit of mouthing.
Jayfeather - A user with an attitude!
Hollyleaf - A user who is too obsessed with the Warrior code.
Lionblaze - A user who refuses to be beaten in battle.
Medicine Cat Gatherings - Every Wednesday, 6:45 PM, EST.
Gatherings - Every Saturday, roughly 6:00 PM, EST.