All wire for electrical use is sized by gauge. Typical home wiring is generally either 14 or 12 gauge.
The smaller the number, the larger the wire diameter. Stranded wire has a slightly larger diameter than solid wire of the same gauge.
Stranded Wire Advantage
Stranded wire is more flexible and easier to pull through conduit. For this reason, large wire sizes are made of wire strands rather than a single wire.
Most wires larger than 8-gauge are stranded wire and most electricians will use stranded wire if 10 gauge or larger has to be pulled through conduit.
Solid Wire Advantage
Solid wire is cheaper to manufacture. Standard wire sizes are still flexible enough to be used in home wiring, so most 12 and 14 gauge wiring is done with solid wire.
Solid wire can also be used for push in type connections found on many receptacles and switches.
The slightly different sizes of like gauges of solid and stranded require different tools. Most wire strippers for stranded wire have red handles and solid wire strippers have yellow handles.
Practicality of Stranded Wire
Gauge 4/0 wire is about an inch in diameter and is always stranded copper or aluminum wire. Bending a single solid strand of this wire would be similar to bending an inch thick rod of copper and would require special tools.