Explain this to me like I've taken high end painkillers for intolerable pain resulting from an old auto accident...which I have.
"An arcanist casts arcane spells drawn from the sorcerer/wizard spell list. An arcanist must prepare her spells ahead of time, but unlike a wizard, her spells are not expended when they're cast. Instead, she can cast any spell that she has prepared consuming a spell slot of the appropriate level, assuming she hasn't yet used up her spell slots per day for that level."
Does this mean an Arcanist can memorize spells X, Y, and Z but decide to cast all X OR Y OR Z instead?
Yes.
Say in his spellbook at level 1 he has five 1st-level spells, A, B, C, D, and E. He can prepare two of them, so say he prepares A and B. Then, he can cast three spells that day (including his bonus spell for his high Int,) so he can cast A three times, cast B three times, cast A twice and B once, or cast A once and B twice.
Excellent! Thank you for your help!