Moria was ordinary and plain - so much so that the ageless look was not obvious. She was not considered graceful and had a thick accent. She wore plain blue wool.
Strength and Abilities
Being a Sitter in the Hall for a while means that Moria was also a high ranking sister and a strong channeller by Aes Sedai standards. Thus she had the strength needed to use the travel weave.
This is not confirmed by "The Wheel of Time Companion" where her level of strength is described only as 25(13). But this is probably a mistake because this is the level of an Aes Sedai with an average strength, and 12 levels below the strongest Sitters would mean that Moria was a too weak Sitter compared to them.
Moria's true level of strength can be guessed by the time she spent as Novice and Accepted which was in total fifteen years, roughly the same as sisters that are at level 19(7), in fact the time spent in training usually reflects the strength of an Aes Sedai.
Moria was born in the year 840 NE and went to the White Tower in 854 NE. After spending eight years as Novice and seven as Accepted she was raised to the shawl in the year 861 NE. She was raised a Sitter in 999 NE, in Salidar.
She was from Illian and had been Aes Sedai for over one hundred and thirty years. She was a tough woman that would balk at little if she believed it was necessary. Anaiya thought she could be harder, or at least tougher, than Lelaine. When Egwene discovers Moria is black, she is shocked and a little saddened, as she had come to rely on Moria for support on many of her motions in the Hall.
She allied herself with the Rebel Aes Sedai and was elected as a Sitter to the Rebel Hall of the Tower to replace the Blue Sitter who had been killed in the Schism. She was not part of Lelaine's faction, despite also being a Blue. She disliked the openness of the Schism, and wished there were some other way to fight against Elaida.
She suggested stopping the soldiers' pay when the Rebel Aes Sedai ran into money troubles. This would have doubtless resulted in them losing their army.
She was one of only two Sitters newly elected to the Rebel Hall that was not traditionally too young for the position, the other being Romanda Cassin. This was related to the mystery of the Too Young Sitters. 
Vote for War
She voted yes on the Rebel Aes Sedai declaring war on Elaida do Avriny a'Roihan. Her open outburst at Lelaine Akashi causes her and Lyrelle to vote "yes" as well, resulting in a lesser consensus standing and a passed motion. Lelaine does warn Moria that they will speak about proper decorum later on.
Black Tower Alliance
She, Malind Nachenin, and Escaralde called a Sitting of the Hall to discuss the findings of the team of Aes Sedai that went to research the events at Shadar Logoth during the cleansing of saidin. These three Sitters were, in truth, seeking a vote on an alliance with the Black Tower. When proposing to ally with the Black Tower, Magla Daronos almost got into a fist fight with Moria.
Ties to Black Ajah
Verin Mathwin's notes on the Black Ajah named her as a member, which was subsequently confirmed at a meeting of the Rebel Hall. After Sheriam is revealed before the Hall, she tries to flee, but Egwene, predicting it, stopped her. She was one of the fifty executed Black sisters in the rebel camp.