1. To show that something exists or is true or valid.
2. To certify by signature or oath
Remember how during your college or school admission days you had to get your documents attested by a gazetted officer in order to be able to submit them for consideration. Those were done so to authenticate their validity or genuineness.
1. She attested to the fact that she saw the murder being committed.
2. In order to be able to prove your identity you need to get these documents attested by a high ranking official.