The quality of the hair is often specified.
Virgin Hair indicates that the hair hasn't been colored or processed in any way. The "Virgin Hair" is collected by tying off the hair to maintain the direction of the cuticle and then cut. After the hair is cut and collected, it can be sewn on a weft, pre-bonded, made into wigs or left in bulk form.
Remy is a term used when all of the hair is human plus when 'close to' all of the strands (e.g. in one weft) are strictly organized with the roots in one direction and the tip to the opposite end. Remy Hair, in general, lasts much longer than Non-Remy and tends to stay shiny and "tangle free" longer. This is based on the fact that every strand of hair is biologically keratinized skin cells organized in layers, overlapping one another. However, this description is no longer accurate. The word "Remy" is being abused in the market, and generally accompanies processed packaged hair.
Single Drawn is of a slightly lower quality than Double-Drawn Hair. The hair will have up to a 2" difference in the tips; that is, some hairs will be up to 2" shorter than their original lengths.
Double drawn indicates that the collected hair of a certain length has all of the shorter hair in the bundle manually removed twice, hence the 'double' drawn. This means that hair extensions that are double drawn will have (nearly) as many hair strands at one end as the other and appear much thicker and not wispy at the ends. This process is very laborious, and therefore makes the extensions very expensive.