Power gems

Power gems are a specific type of gem - they do additional damage to your opponent after your turn ends.

If you're talking about special gems specifically, I can break them all down:

Damage Modification

• Power gems do what I described above - Do extra damage (each gem doing X amount of damage) on top of any damage you dole out that turn every turn they remain unmatched or unmodified on the board.
• Protect gems do the opposite, protecting you from X amount gem damage from opponents during their turn. This includes power and leech gem damage (though leech gems will still heal for the normal amount).
• Leech gems do nothing until they are broken, upon which they both damage your opponent for a set amount of damage (on top of the damage the gem would normally do) while healing you for the same amount of health. Leech gems don't give you health if there's no more health to steal, however - an opponent in danger won't give you health when you match leech gems.
• Multiply gems multiply everything that gem can do by a certain multiplier. This doesn't just apply to damage, but MP gained and notches on the pin bar moved as well. So a blue x4 gem will do 4 times as much damage as a normal blue gem, give you 4 blue MP, and move the pin bar 4 notches, as opposed normal damage, gaining 1 MP, and moving the pin bar 1 notch with a normal blue gem.
• Heal gems heal you for X amount of damage when broken. While they give out MP like normal gems, they do no damage, instead just healing you.

Opponent Disruption

• Silence gems make it so that when the opponent matches that gem, they do not gain any MP of that color for that gem. This only applies on a by-gem basis - if you match 3 purple gems and two are silence gems applied by your opponent, then you only gain 1 purple MP. If you created those silence gems, then you gain the full 3 MP.
• Botch gems make it so that when the opponent matches that gem, they do not do any damage with that specific gem. Much like with silence gems, the damage reduction is only per-gem (a 3 black match with 1 enemy black botch gem will only do the damage of 2 black gems) and only applied when the botch gem belongs to your opponent. This damage also does not apply when attempting to kick out.

Board Modification

• Color Turn gems change into a random color at the beginning of the turn of whoever spawned them. This allows for additional matches before your turn even starts, potentially giving you more damage or MP to work with before you actually make your move. These matches also affect the pin bar, however, and can cause a pin before you can even move. Color turn gems also change colors during every turn the player who spawned them is in a pin or submission.
• Immobile gems prevent the creator's opponent from moving that gem in any way, preventing them from making certain moves. They are still affected by board gravity and can be destroyed using any other means, but they cannot be shifted by swapping gems.
• Reinforce gems do not disappear from the gem board when broken, instead becoming normal gems. This allows these gems to be broken twice before disappearing from the board. These gems work identically for both sides - a character can create reinforce gems and both they and their opponent can break them, turning them into normal gems.
• Freeze gems lock a gem into the state it was in when it was frozen, preventing any further modification. This is typically used to prevent characters from modifying the board, but can also be used to lock down special gems - a multiply gem that's frozen works like a normal multiply gem, but can't be modified or stolen. Much like reinforce gems, both sides cannot modify a gem once it has been frozen, regardless of who created them.
• Snowfall gems modify all gems below them into becoming the a given type of gem when matched - this can be the same color of gem (make all gems below the snowfall gem into blues), or modifying them to become a certain type of special gem (make all gems below the snowfall gem into botch gems). The transformative properties of snowfall gems are halted if there's a freeze gem in the the snowfall gem's path.
• Pyro gems work identically to snowfall gems, except they modify all gems above them to the specified type of gem.

Board Destruction

• Blast gems destroy all gems adjacent to them, causing a 3x3 area to be destroyed.
• Row Break gems destroy all gems in the same row as the Row Break gem.
• Column Break gems destroy all gems in the same column as the Column Break gem.
• Cross-Break gems destroy all gems in the same row and column as the Cross-Break gem.
• X-Break gems destroy all gems to the diagonals to the X-Break gem.

Trigger-Based Gems

• Countdown gems begin a countdown, the counter ticking down by 1 at the beginning of the turn of whoever created them. Countdown gems also count down during every move the creator is in a pin or submission. Once that counter hits zero, the countdown gem's effects come into play. Details as to what the countdown gem does can be found in the description of the move that creates them.
• Juggernaut gems operate similarly to countdown gems, but also produce a secondary effect every time they count down - the primary effect still occurs when the countdown hits zero. These gems are also reinforced, requiring two breaks to eliminate. The countdown still persists and does not change upon the first match.
• Trap gems activate when matched, producing two unique effects - one when the character creating them matches them, and one when the other character matches them. Each effect can be found on the description of the move that creates the trap gems. These are the only gems that are hidden from the opponent on the board - to the opponent, trap gems merely appear as normal gems.

There's a lot of special gem types in this game and hopefully I explained all of them - let me know if I missed any or if you have any questions.

Getting on translating mode! thanks