Nayru the Oracle is the Oracle of Time. That's why some people belive Nayru to also be the goddesses of Time. It's like the greek's mythology. Poseidon is the god of the sea, but he's also the god of eathquakes, of horses and of a bunch of other things
The term "oracle" dates back to ancient Greece, in terms of someone who has a close connection with the Gods. For example, the Oracle at Delphi has a close connection to the Greek god Apollo, acting as their messenger of sorts on earth. I think Nintendo took a bit more simplistic route by naming the Oracle Nayru to demonstrate her connection to the Goddess Nayru, or the Oracle could merely be a physical representation of the goddess Nayru; personally, I believe it is the former, but it works either way.
The reason I think Nayru is associated with time is a vague connection, as TheGermanLegend pointed out. The same is true of Din having a connection with the seasons in OoS. Take a look at this quote:
Zelda said:
Din, the goddess of power...
Nayru, the goddess of wisdom...
Farore, the goddess of courage...
Din...
With her strong flaming arms, she
cultivated the land and created
the red earth.
Nayru...
Poured her wisdom onto the earth
and gave the spirit of law to
the world.
Farore...
With her rich soul, produced all
life forms who would uphold
the law.
The term "law" could be a reference to the "laws" of nature, one of which being time, among things like physics, etc.
Similarly, Din has an association with the Seasons because she "shaped the land," which demonstrates a connection to nature.