Sympathetic Law

The sympathetic law of magic is very old. Several thousands of years old. This also means that it holds great power as it can draw on all that time of being used. It states that the part always carries a connection to the whole.
A piece of hair, a nail, or blood from someone can stand in for that person to some degree. In the same way, knowing someone's name is knowing part of them. The same goes for paintings of someone's likeness, a place that they hold dear, etc. The more and stronger connections you have access to, the easier it is to create a connection to the person, place, object, or otherwise, that you're trying to reach.
When a ritual attempts to affect or study someone or something, sympathetic bonds can be used to tie it to the right target. This is why Voodoo dolls might have hair and toenails and why Kabbalah places a lot of emphasis on the words representing power, for example.
Those who are aware of how arcane rituals work are often very wary of leaving any parts of themselves behind anywhere.