In One Piece world everything has an spirit, this spirit is a type of energy that flows and usually is peaceful, it can be sent and usually doesn´t affect the physical world but some people are able to manipulate it transforming it into energy to the physical world.
Some hakis are more powerful than others since they are able to overshadow others, imagine a group of winds coming from everything and one of the living things is able to make a wind that flows away this energy, since this energy is needed to keep the person conscious when it is blown out then the person becomes unconscious.
The haki can be used in different ways:
-It can be projected into a weapon, punch or clothes to increase their strenght several times.
-It can be used as a blocker against another attacks and elements of the nature, in this case the haki (that is like a type of energetic wind) puts a barrier that can´t be crossed by the haki of the attack and becomes deflected.
The reason is that even the akuma no mi have this type of energy that can blocked, when Luffy was damaged by the Sentoumaru first and the boa sisters later was because their haki overshadowed Luffy devil fruit haki (not luffy one) and he lost the properties of the rubber for a second. The devil fruit is making enery in continous form, when Kurohige grabs his enemies then the haki of the devil fruit becomes absorbed in continous form by the gravity putting it away from the devil fruit user. Devil fruit users can increase the haki of their devil fruits with their own haki.
For example, imagine Crocodile developing haki and using his own haki to increase the strenght and the increase of his attacks and even making himself invincible to his own main weak point (liquids) making him stronger.
Why some users are able to predict movements? Rayleigh named Haki the voice of all things and revealed to Robin that Roger was unable to read the Poneyglyphs, then the voice of all things must the the language of the wind-haki, the wind singing, a language that tells the truth about everything and the ones able to manipulate the haki are able to understand it.