A digital signature is quite different from a normal signature. Someones normal signature is always the same, and independent of the document signed. However, a digital signature is different for different documents. It's closely related to encrypting the document, except that in this case, you don't encrypt the plain text, but you encrypt a digest, and attach the encrypted digest to the document. The digest can be decrypted using your public key (assuming you are using some well-known public/private key encryption technique, like PGP).

Assuming the encryption algorithm can't be broken, and your key isn't compromised, noone else can create the signature. The signature can be copied, but the signature is worthless without the plain text, copying to another document doesn't sign it. Also, if the original text is modified, it no longer matches the signature, so it prevents someone from modifying the original document and pretending you signed it.

Abigail