Gems are a completely new and very useful item type in Diablo II.  Functionless on their own, gems possess great power when utilized with a weapon, shield, or helm, bestowing potent magical enchantments upon the item and its wearer.  Gems make normal items magical, adding a wide variety of effects, such as elemental resistance, mana and hit point drain, and fire damage.  There are seven different types of gems, Amethysts, Diamonds, Emeralds, Rubies, Sapphires, Skull Gems, and Topazes.  All have different effects depending on what sort of item they are "socketed" in.  There are five levels of quality for gems: from worst to best they are, chipped, flawed, normal, flawless, and perfect.

Gems can not be bought, only found (this has changed several times during development, but seems to be set now) and only the lower quality ones are dropped, at least in the beta.  Blizzard has said that there will probably be higher quality gems dropped later in the game, but never perfect quality.  Only normal (non-magical) items with sockets can hold gems, and such these are rare, but not extremely.  The one semi-exception to this is that wands, staves, and scepters can have random bonus to skills, but they are class specific.   Necromancer spells on wands, Sorceress spells on staves, and Paladin skills on scepters.  These items can also be socketed, and can be considered "magical" though they'll never have prefixes and suffixes with sockets.

So there are no true magical or Rare items with sockets, though it is possible that there might be some Unique or Set Items that would hold gems.  None are known though, and it seems like such an item would be overpowered and unbalanced, so most likely none exist.

Only weapons, helms, and shields can have sockets.  No body armour, boots, gloves, belts, or jewelry will ever be socketed, not even Uniques.  Socketed items have a maximum of three sockets, and the number is determined by the item type.  Longer weapons can have up to three, shorter weapons two or one, while helms have only two, and shields have two.  (At least in the beta, possibly in the full game there are higher level helms and shields that have more than 2 sockets.)

Once a gem is inserted into a socket, it is there forever, and can't be upgraded in quality, so be sure you want to put a gem in before you do.

So what do gems do?  Their effects vary, but are logical: Gems placed into weapons generally add elemental damage, while gems in shields provide resistance, and gems in helms add to hit points or other attributes.  Exactly how much benefit a socketed gem provides depends on the quality of the gem.  There are five purity levels of gems.  From best to worst: Perfect, Flawless, Normal, Flawed, and Chipped.

   

   Diamond
   Emerald
   Ruby
   Sapphire
   Skull
   Topaz