What is an oracle? What is it that Ferdinand believes even against an oracle in The Tempest?

In ancient Greece, an oracle was a gateway to the will of the gods. It was a place that, for a fee, people could consult with a priest or priestess, through whom the gods spoke, to receive prophecies and advice from the gods. The most famous (and most expensive) oracle was the Oracle of Apollo at Delphi, which was established in the eighth century BC.
Unfortunately, the information that the oracles provided was often cryptic and confusing—and sometimes even contradictory—and it was up to the individual to figure out exactly what the oracle meant.
A side business grew out of this for "prophets" and "seers" (like Teiresias in Oedipus Rex), who would interpret the oracle's information for a fee.
As far as Ferdinand in Shakespeare's The Tempest is concerned, the oracles were considered to be absolutely truthful and infallible.
In act 4 of The Tempest, Prospero gives Fernando permission to marry his daughter, Miranda, and Prospero praises Miranda to him:

PROSPERO: . . . Here, afore Heaven,I ratify this my rich gift. O Ferdinand,Do not smile at me that I boast of her,For thou shalt find she will outstrip all praise,And make it halt behind her.
FERDINAND: I do believe itAgainst an oracle.
PROSPERO: Then, as my gift and thine own acquisitionWorthily purchased take my daughter (4.1.7–15)

Prospero wasn't telling Ferdinand anything he didn't already know and believe. Ferdinand had already met Miranda, fallen in love with her, and seen for himself the remarkable person she was.