I'm pretty sure he is referring to stranded wire as in wire that's like a rope as opposed to solid core wire which is just a solid piece of metal for a wire. Think of a rope vs. a solid pipe.
In general the solid core can carry more current, but it's much more expensive and hard to work with because it's so stiff. Stranded wire is stronger (tensile strength), more malleable (flexible w/out breaking), but the strands get in each other's way under load and prevent as much current from moving down the cable as a solid core wire can move. In general, 15A or more is usually a solid core wire in your home, but it doesn't have to be a solid core wire to carry 15A. That depends on the gauge (thickness in 1/x of inch ie. 8 gauge = 1/8 inch thick). The higher the gauge, the more current you can run down the wire. The wire should have an Amp rating on it to help you decide which gauge to use.