The bead is the stiff, fabric-covered cord that forms the inner circumference of the tyre and helps hold the tyre onto the rim
The bead is made using steel wire which forms a stiff, durable bead. These tyres cannot generally be folded and will be usually despatched in a large bag.
Folding tyres use a synthetic fibre such as Kevlar, which is equally durable but more flexible. These tyres can be folded. Unlike the stiff steel bead of a regular tyre, folding tyres generally come in a compact bundle.
Whilst this is certainly an advantage for packaging, manufacturers originally designed folding tyres for long-distance touring cyclists who needed to take extra tyres on their trips.
Folding tyres are also usually better quality than their wired counterparts and they generally weigh less than regular wired tyres. (Reducing the weight of a cycle tyre and wheel makes riding much more efficient because of the energy required to keep the wheels spinning.)