A digital signature (not to be confused with a digital certificate) is an electronic signature that can be used to authenticate the identity of the sender of a message or the signer of a document, and possibly to ensure that the original content of the message or document that has been sent is unchanged.
The idea behind digital signatures is the same as your handwritten signature. You use it to authenticate the factthat you promised something that you can't take back later. A digital signature doesn't involve signing something with a pen and paper then sending it over the Internet. But like a paper signature, it attaches the identity of the signer to a transaction.
Digital signatures require the use of public-key cryptography. If you are going to sign something digitally, you need to obtain both a public key and a private key. The private key is something you keep entirely to yourself. You sign the document using your private key, which is really just a kind of code. Then you send the document to the receiver, who needs to verify your signature using your corresponding public key. He uses your public key to make sure you are who you say you are. The public key and private key are related, but only mathematically, so knowing the public key makes it possible to verify your signature without knowing your private key. In fact, it's nearly impossible to figure out your private key from your public key.
