There are several implications in the statement that the Trojan women went to the temple of Athena to make supplications.
For one, Troy and Greece are culturally quite similar. Since the publication of Edward Said's Orientalism, there have been some scholarly attempts to portray the Trojans as quite different from the Greeks, with a culture reflecting Western stereotypes about "the East" in its luxury and decadence. However, Homer makes Greek and Trojan customs very much the same, particularly in religious matters. Both sides worship the same gods in the same way, and ask them for the same things.
Another implication is that the Trojans do not know that Athena favors the Greeks. Athena is the goddess of wisdom, and the particular patron of Odysseus, the cleverest of the Greek warriors at Troy. She is implacably opposed to the Trojans, so their supplications will fall on deaf ears. An alternative explanation here is that the women think their prayers may change Athena's mind.
This quote also implies that women played an important part in formal religion. Aside from the central mission performed by these women, Chryseis, Briseis, and Cassandra are all priestesses.
Finally, this implies both sides expect the gods to intervene in the war. In fact, despite the frequent interventions of the gods, they do not have much effect in the long run. Zeus, the most powerful of the gods, supports Troy, but allows it to be destroyed anyway. Nonetheless, the participants expect divine intervention and believe it to be of great importance.