Hope this look back on the basics of Harry Potter words helps. These come up in the new one.
Auror: a law enforcer for magical communities
Acchio: magic word used in the summoning spell, sometimes followed by the object of the magic. For example, if you want to refill your cup without crossing the room, you could point and say "acchio coffee pot" to make it fly into your hand.
Apparate: to teleport. This is what the characters are doing when they appear and disappear amid those swirly special effects.
Deathly Hallows symbol: line bisecting a circle inside a triangle to represent a wand, stone, and cloak. Gellert Grindelwald is known to have worn this symbol to signify his search for the Hallows.
Grindelwald, Gellert: dark wizard who became friend and later rival of the famous Albous Dumbledore. (Dumbledore and Grindelwald are a lot like Professor X and Magneto.)
House Elf: Indentured creature with extremely powerful magic compelled to obey human landlords.
Legilimens: the spell for reading minds. Also a person who practices said spell. (Not mentioned: Occlumency, the method of resisting the mind-reader.)
LeStrange: Surname of a pureblood, dark wizarding family.
Relations of Bellatrix LeStrange played by Helena Bonham Carter in the HP movies.
MACUSA: "Magical Congress of the United States." (Apparently that's stated right in the movie but I missed it.)
Muggle: a non-magical person, also called a no-maj (sp?) in the States.
Obliviate: the spell to selectively erase a subject's memory or the act of using said spell. Often used by official wizards on witnesses to supernatural occurrences.
Obscurial: Far as I know this term wasn't mentioned in the main stories. I'll let you find out what it means by watching the new movie.