Attestation is the act of bearing witness. It can take a number of different forms in a legal sense. Generally speaking, it refers to an activity in which someone confirms something with a written or oral oath. A simple example of an attestation might be a signature on the bottom of a legal document from a notary public indicating that he or she saw the author write out and sign the document.
In some cases, an attestation is simply a verification that a document was signed in front of witnesses. By signing, the witnesses attest that they saw the document being signed and were aware of the identity of the signatory. They are not, however, attesting to anything in the document itself; the document may be incorrect or improperly filled out, for example, but this is not the responsibility of the people who attested to it.