Synchronization

1
The ability to sympathize with other people. Putting it simply, it's giving one's own physical strength to somebody else.
As Kohaku and Hisui are particularly talented sympaths, they don't just give their own physical strength, but also strengthen and support the mental and physical strength of their target.
Also, because this is sympathy and not empathy, even if the target is injured there won't be any feedback for the sympath.
The method of sympathizing varies depending on the practitioner. For some, it is possible to sympathize regardless of the target's will, while for others some sort of ritual is necessary.
The ritual is a switch on the spiritual plane passed down within a family, to control heretical abilities. It is a mental block implanted in the subconscious that prevents the ability from activating unless certain conditions are met.
……In other words, Kohaku and Hisui's family must have been a bunch of perverts, huh?

Tsukihime Data Collection: Tsukihime Dictionary
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① The ability to transfer energy to another person. Those who excel at using this ability can even improve the physical prowess and mental fortitude of the recipient.
② While is it possible to transfer energy to a recipient under normal circumstances (without the explicit desire of the recipient, or without doing anything special), there are those with the synchronization ability that require some kind of ceremony to be performed. This acts as a safety lock for the powers of demon-children and individuals with special abilities because of the persecution or abuse they could face (if their powers were to be discovered).
③ The ceremony is a mechanism to allow the synchronizer to remove the subconscious safety lock placed on the ability. Ceremonies differ from family to family.

Colorful MOON Tsukihime: Tsukihime Glossary
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The ability to sympathize with other people. Putting it simply, it's giving one's own physical strength to somebody else. (Synchronizing with somebody else would be empathy.)
As Kohaku and Hisui are particularly talented sympaths, they don't just give their own physical strength, but also strengthen and support the mental and physical strength of their target.
Also, because this is sympathy and not empathy, even if the target is injured there won't be any feedback for the sympath. In game terms, it's like turning off collision detection.
The method of sympathizing varies depending on the practitioner. For some, it is possible to sympathize regardless of the target's will, while for others some sort of ritual is necessary.
The ritual is a switch on the spiritual plane passed down within a family, to control heretical abilities. It is a mental block implanted in the subconscious that prevents the ability from activating unless certain conditions are met.
……In other words, Hisui's family must have been a bunch of perverts, huh?

Tsukihime Dokuhon Plus Period: Tsukihime Dictionary Revised
Translator's Notes
  1. ^ Sometimes also translated as “Sympathy” or “Synchronization Ability.” Note that while “Synchronization” may sound like a two-way ability, this is actually just a one-way ability, giving strength without any feedback from the target.