Assuming you're already broadly familiar with the Harry Potter films and Wizarding World in general, these are the things that you'll need to know prior to seeing FB2 in order for the film to make sense (since these plot-points aren't directly addressed in dialogue).
Obviously everything below this line is a massive spoiler for the first Fantastic Beasts film.
1) It seems to be assumed that you already know that Gellert Grindelwald is an evil wizard who (unsuccessfully) tried to take over the world in the 1940s. He fought against Albus Dumbledore in a famous duel and was vanquished. Dumbledore and he had an intimate (possibly sexual) relationship in their teenaged years.
2) Newt Scamander is a 'magizoologist' who specialises in the care and study of magical animals. He traveled to New York in the previous film and encountered a young boy (Credence Barebone). Due to his abuse at the hands of his adopted mother, the boy had developed an affliction that affects wizards who deny their magic, called an Obscurus. Normally an Obscurus will erupt from a child and kill them, but not before wreaking damage on their surroundings. Credence's Obscurus is unusually (abnormally) large and powerful.
3) Nagini is the snake owned by Voldemort in the previous films. It's his loyal servant and, as far as we're aware, just a normal (albeit magical) snake.
4) Newt met a Muggle (No-Maj) called Jacob who basically functioned as his comic sidekick in the previous film. At the end of the film this character had their memory erased.
5) Newt encountered a witch called Tina Goldstein. She was investigating the abuse of the boy Credence despite having been told by her superiors to leave well enough alone.
6) Newt and Jacob spent time with Tina's sister Queenie, a witch with an abnormal talent for mind-reading. Newt fell in love with Tina. Jacob fell in love with Queenie.
7) Grindelwald spends most of the film impersonating a wizard working for the American Ministry of Magic. At the end of the film he is revealed and captured by Tina and Newt working together.
8) At the end of the film Credence appears to die.
9) Newt appears to have had a crush (or previous relationship) with a witch called Leta Lestrange. He carries a picture of her with him.