As Joachim so perfectly summarized it a digital signature uses asymmetric encryption protocols along with hashing to provide security mechanisms in the validation of a signature. This needs to be differentiated from the more general term of electronic signature which can be anything that can be considered a signature(A scan of your signature, a typed signature in your computer, etc).

For example in the US the use of electronic signature standard is based on a mutual agreement between parties and the use of digital signatures is not enforced since the security of an encryption cannot be completely guaranteed (you only have the assurance that it has not been broken until a moment in time, it does not imply that tomorrow the encryption can be compromised).

In this sense the legal requirements of a digital signature are the same as the electronic signature and the physical signature, you have to trust  the signature generation protocol in both instance and that nobody violated the protocol through forgery. What differentiates one from the other is in  the methods of proving authenticity and the protocols that were followed in its generation.

digital signature basic principle where explained above

digital declaration is the next step of it; elliptic curves provide better performance rate

The digital signature is the computer-typed equivalent of handwritten signature. Even though there are similarities between handwritten and digital signatures there are also elemental dissimilarities. The main similarity is that both kinds of signatures can give proof of authenticity of the document. The dissimilarities are because of the fundamentally different nature of paper typed documents on the one hand and digital documents on the other. In paper-typed transactions the document contains text printed as ink on the piece of paper, where a text denotes the information and the paper denotes a storage medium. In this means the information and the storage medium are always together. The validity of the paper-typed document is authenticated by the signature written in ink on the same piece of paper. The signature serves as proof of the signer’s agreement to the content on the paper, and the verification of signatures can be completed directly without any complex tools

For digital signatures all of this changes. Documents are irrelevant since the information is denoted by logical bits that can be stored on, and copied to, any appropriate e-medium, and they only become meaningful to persons if denoted by an analogue physical medium such as the computer screen. The validity of the digital document is authenticated by checking that the digital signature logically equals the bit string representation of the document. Since, the digital message in its bit string form cannot be understood directly by the signer, the digital signature must only serve as evidence of the signer’s agreement to the high level semantic interpretation of the message, although technically it denotes the signer’s agreement to the bit string message. For signers, digital signatures must be interpreted as an agreement to the analogue representation of documents, such as the computer screen. Highly complex tools are now required not only for interpreting the message but also for making the digital signature. The complexity of the tools required to interpret and imagine the digital message determines the semantic distance between its bit sting representation and its semantic interpretation. It is relatively easy to change the interpretation of a digital document by implementing changes on the computer system where the document is being processed, and the greater the semantic distance, the easier it gets. From a semantic perspective this creates uncertainty about what exactly has been signed.