Sliver means: A strand, or slender roll, of cotton or other fiber in a loose, untwisted state, produced by a carding machine and ready for the roving or slubbing which precedes spinning.. There is no real cause for parental concern; it is descriptive vocabulary rather than risky behaviour. If your teen uses it, context will usually make the intent clear. A short, curious question about where they heard it is usually all that is needed to know whether to follow up.