Kenbunshoku Haki allows the user to sense another person's aura/precense, also allowing the user to predict that person's movements/attacks. Taking the sensory ability further a trained user can also sense a person's emotions and how strong or weak they are.
Busoshoku Haki allows the user to create an invisible forcefield around himself, enabling the user to defend himself from attacks that might've hurt him otherwise, and the ability to touch and harm Devil Fruit users, even Logia's. Similar to the first form, there is another ability that can be attained through training, which is the armor physically altering the user's body, or hardening it, where the entire body or just a single part appears to be covered in a black metal.
Haoshoku Haki, the rarest form or King's Haki, allows the user to intimidate/dominate others by knocking them out. (Like two will's clashing, and the stronger overcomes the weaker) This is the ONLY form of Haki that a person can't gain through training, but must be born with.
If you're talking about Luffy then yeah we've known for a while that he had the final type, but I can't remember whether or not Law was ever around when he used it.