A remnant is something that's left over, once the rest is used up. If you plan to sew a shirt using only a remnant, it might have to be a midriff shirt.
The noun remnant can also be used to refer to leftover things other than cloth. The origin of the word might help you remember this, more all-purpose, meaning — it comes from the French remanant, which means "to remain." Think of it this way: a remnant is something that remains, or is left behind. For example, the remnants from the ancient battle gave archaeologists clues from which to infer what had happened.