Capcom has seen it fit to explain in detail the much-hyped gems system in Street Fighter X Tekken on their developer blogs. The explanation is lengthy, of which I will attempt to condense here for easier reading.
Essentially, all characters in Street Fighter X Tekken will have three empty slots for gems, which are broken down into Boost gems that increase stats given certain criteria and Assist gems that likewise give a boost but are activated passively and immediately without needing to satisfy any requirements. (Click here for a full list, though its subject to change.)
Both Gem types, however, can have downsides. Some gems don't have any downsides apart from gaining, say, 10% attack power if you land 5 normal hits, but that's usually only if the gem's rank is a measly Level 1. Gems at a higher level are much stronger, but require a higher requirement cost (in this example, say 10 normal hits to activate) and can decrease other stats like speed. One Assist gem in particular called Auto-Block may be a huge boon for beginners, but every time you block, it decreases the special gauge by a block, and if the gauge is empty, that means no Auto-Block. That's a hefty price to pay for veteran players.
Since all gems have a different level and all Boost gems have a different activation method, equipping characters with the right trio of gems means getting the gems that best suit your style of play and your tag team of choice. It's also important to consider the combination of gems, since the right mix can cancel out the negative effects of any gems.
Different retailers (Amazon, GameStop, Best Buy) will offer special packs for gems, some of which take two gem slots to use: GameStop's World Warrior Pack, Amazon's Iron Curtain Pack, and Best Buy's Lightning Legs Pack. The Special Edition comes with the King of Iron Fist Pack, and pre-ordering it will get you the Cross Arts Pack. This might be a point of contention, because it might give some players an advantage over other players only due to paying more money. Hopefully, the in-game gems will be more powerful than the gems in the packs.