Definition
A blue gem is a Case Hardened skin whose pattern index lands on a seed that renders an unusually large amount of blue. Case Hardened is a steel finish that mixes blue, gold and grey across the model, and the seed decides exactly where each colour falls. Most seeds produce a mostly gold-and-grey blade with a little blue; a small handful flood the visible surface with blue. Those are the blue gems.
The term isn't official — Valve never labels a skin "blue gem." It's a collector convention, with community databases tracking which seeds on which weapons show the most blue and ranking them into tiers. The blue can appear on the playside (the face you see when the weapon is equipped), the backside, or both; a seed that's blue on the playside is worth far more than one that hides its blue on the back.
Why blue gems are worth so much
The value comes from the pattern index being fixed at drop and impossible to change. A given weapon has only a few thousand possible seeds, and only a tiny fraction read as full blue gems, so supply is permanently capped at "however many of that exact seed have ever been pulled or crafted." Demand from collectors is steady, so prices sit far above a normal copy of the same skin.
On a blue gem the seed swamps almost everything else. Float and wear tier still matter a little — a clean Factory New gem beats a beaten Battle-Scarred one — but a top-tier seed in a worse condition still outsells a generic seed in Factory New. The famous example is the AK-47 Case Hardened, where seed 661 is the most coveted playside gem and trades for orders of magnitude more than a random AK Case Hardened. Knife blue gems (Karambit, M9 Bayonet) and pistol gems (Five-SeveN, Glock) follow the same logic. The full tier lists and how to read your own seed are in the Case Hardened blue gem guide and the patterns, floats and wear pillar.