These are Game Terminology for things that are either more or less effective at causing damage to a specific type of creature. They can come in many different forms, but are typically a certain type of weapon, magic, location, or item.
They can also very in how effective they are. Some weaknesses may cause instant defeat while others may do a percentage more in damage. This is also true with Resistances, as some may cause full immunity while others only lesson the amount of damage taken.