Today, they are a fundamental component of business in cyberspace. And numerous laws, state and now federal, have codified digital signatures into law. These laws are a mistake. Digital signatures are not signatures, and they can't fulfill their promise.
Understanding why requires understanding how they work.
The math is complex, but the mechanics are simple. Alice knows a secret, called a private key. If the verification calculation checks out then Alice must have signed the document, because only she knows her own private key. Mathematically, it works beautifully. Semantically, it fails miserably.