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Runes and gems are used in the Workshops to give additional bonus modifiers to your pieces of equipment.

The number of gems/runes that can be added to a piece of equipment is limited by the type and level of the equipment; i.e. you can only get four available slots on Legendary equipment. In addition, you can't add a gem/rune of higher class than the equipment you are adding it to, nor can you add more than one of any gem/rune type to the same piece of equipment.

Gems can be obtained by attacking invaders, completing tasks and yielding resource spots.

Gem Type Gem Purpose Simple Usual Unusual Rare Epic Legend.
Taaffeite All Troop Offense 1% 2% 4% 6% 8% 10%
Tourmaline All Troop Defense 1% 2% 4% 6% 8% 10%
Ruby All Troop Health 1% 2% 4% 6% 8% 10%
Rhodonite Melee Offense 1% 2% 4% 6% 8% 10%
Smoky Quartz Melee Defense 2% 3% 5% 7% 9% 12%
Spessartine Melee Health 2% 3% 5% 7% 9% 12%
Opal Cavalry Offense 1% 2% 4% 6% 8% 10%
Onyx Cavalry Defense 2% 3% 5% 7% 9% 12%
Almandine Cavalry Health 2% 3% 5% 7% 9% 12%
Spinel Ranged Offense 1% 2% 4% 6% 8% 10%
Aventurine Ranged Defense 2% 3% 5% 7% 9% 12%
Corundum Ranged Health 2% 3% 5% 7% 9% 12%
Jacinth Killer Offense 1% 2% 4% 6% 8% 10%
Pyrope Killer Defense 2% 3% 5% 7% 9% 12%
Rose Quartz Killer Health 2% 3% 5% 7% 9% 12%
Agate Seige Offense 1% 2% 4% 6% 8% 10%
Rubellite Siege Defense 2% 3% 5% 7% 9% 12%
Carnelian Siege Health 2% 3% 5% 7% 9% 12%
Garnet Scout Offense 1% 2% 4% 6% 8% 10%
Morganite Scout Defense 2% 3% 5% 7% 9% 12%
Zircon Scout Health 2% 3% 5% 7% 9% 12%
Aquamarine Learning Speed 1% 2% 4% 6% 8% 10%
Euclase Training Speed 1% 2% 4% 6% 8% 10%
Indicolite Construction Speed 1% 2% 4% 6% 8% 10%
Amber March Speed 1% 2% 3% 4% 5% 7%
Beryl Troop Capacity 1% 2% 3% 4% 5% 7%
Emerald Hero Energy Regeneration 1% 1% 2% 2% 3% 3%
Peridot Hero Energy Capacity 35 90 100 150 200 250
Sapphire Food Production 1% 2% 4% 6% 8% 10%
Amethyst Lumber Production 1% 2% 4% 6% 8% 10%
Lazurite Iron Production 1% 2% 4% 6% 8% 10%
Alexandrite Stone Production 1% 2% 4% 6% 8% 10%
Jasper Silver Production 1% 2% 4% 6% 8% 10%
Topaz Resource Yield Speed 1% 2% 3% 4% 5% 7%

Gems drops can be viewed here:

NOTE/warning: You can buy Diamond Knifes for removal of a mounted gem - note that this knife can only be used ONCE. Since you are offered to buy a range of knifes, but only from the minimum type of knife up to Legendary Diamond Knife, you get the impression that a more expensive knife would be better - but it is not so. Buying a higher type of knife is just a waste of Gold. Only the lowest possible grade of knife are the one you need and you can only use it once!

The knife level is supposed to determine what the highest level gem is you can safely remove without destroying the gem in the process. So for example if you have applied an unusual gem and wish to save it rather then destroying the gem you need the apropriate level knife. That said im not aware of the lower level knives either working to remove gems or if there is a chance of the gem being saved from the use of lower grade knives. You also have the option of just choosing to destroy the gem which doesnt require a knife.