Half-Hard or Dead Soft?
The technical bit:
Most metals are composed of crystals which, when most soft (dead soft) are fairly randomly oriented, and pretty well spaced out. As you work metal (by bending, hammering, drawing, etc.), the crystalline structure begins to re-orient itself into a more orderly matrix, the spaces between them closing up. For jewelry making, Half-Hard and Dead Soft wire are the most commonly used wires. Half-Hard wire has been treated (generally by work-hardening) to make it stiffer and hold shapes better. Dead-soft wire is much softer than half-hard wire of the same gauge, and useful for intricate weaving and wire sculpting where the technique requires reshaping your wire several times (tightening the weave, criss-crossing back and forth around a gem, etc.).
How this information applies to your jewelry:
If youre making wrapped loops, inserting beads into chain, making your own clasps and earwires, or creating wire jewelry components, Half-Hard is the way to go. It is flexible enough to form into whatever shape you imagine, and will hold its shape well even if its in your favorite piece of jewelry and worn every day.
For intricate weaving designs, applying textile techniques to wire and making woven chains from scratch, Dead Soft wire will handle tons manipulation before it becomes brittle and breaks. Dead Soft wire is also wonderful for use in embellishing around a larger bead or component, because it will more easily form to the detailed contours of the original piece