Conk refers to hair relaxers which are also known as "kits".

Conk was the very earliest relaxers that were cooked in the kitchens of African Americans and was made from recipes passed down from generations. 

The Conk was usually made with a lye base that would relax the super coarse texture of the hair.  Unfortunately, the more coarse the hair, the longer the Conk or lye based product would have to remain on the hair and the lye would burn the scalp cause some pain and sometimes it would cause blisters and sores to form on the scalp.  To cool down the lye and slow it down, sometimes mashed potatoes were applied to the scalp.

Malcolm X the great African-American Muslim and political leader had his hair straightened.  However, surprising, even though he had his own hair straightened, in his speeches he would say that he viewed the straightening of hair amongst Black men, known as the conk, as a denial of their Black identity.

In his book, The Autobiography of Malcolm X he described it as "a  step toward self-degradation ... I admire any Negro man who has never had himself conked, or who has had the sense to get rid of it - as I finally did"

In modern times relaxers have been reformulated to make them less caustic and painful.  In some cases lye is no longer a major ingredient.

Relaxers usually come in two formulas which include:

1.  Gentle relaxer for fine, thin or delicate hair or scalps
2.  Full strength relaxer for super coarse hair

One of the strongest relaxers is Bantu which is required for the most coarse textures.  Even when Bantu is applied to the coarsest of hair texture, it may only soften temporarily or not last very long.

To assist with the development of 360 waves in super coarse hair, relaxer can be applied to the entire head OR just to selected sections of the head.  Coarse textured hair may have a more difficult time developing a wave pattern on the sides and near the nape of the neck.

A kit can be used to soften the sides and nape BUT for a reduced amount of time.  Since the sides and nape of the neck are more delicate areas, it is important to use the relaxer for only a few minutes and not for the suggested time.

Do yall think stars like Nelly use wave kits?