The term used for hair extensions that during the production process all the hair remains in the original orientation. It is important for the hair to not be mixed up directional because the hair cuticle at a microscopic level resembles roofing tiles. If the hair cuticle of adjacent hair strands are oppositely aligned then they will stick and grab onto each other. Cheap hair pays less attention to this part of the hair extension processes and results in hair that is constantly tangled and snarled.
Remy is derived from the French word 'remettre' meaning to 'put back.' Remy is the contemporary spelling of 'remis' which was came from remettre. Putting the hair back into its correct allignment and not having any individual hairs inverted in the bundle takes a lot of effort and generally is more expensive. Far too often companies will forgo this process and use an acid wash to take off the cuticle all together. Hair treated this way is often not shiny and loses its luster. Another thing that hair companies do is apply a coating to the hair that at first feels smooth eventually wears off and leaves the hair in a matted mess.
Unfortunately a lot of hair now-a-days goes mislabled due to the inability of people being able to detect the hair orientation. Trusted premium brands are more expensive for a reason.