Asra is very weak in the One Power, in fact Elayne thought that she would probably never be allowed to test for Accepted.
This is confirmed by "The Wheel of Time Companion" where her level of strength is classified 54(42), far below the minimum level of 45(33) to become Aes Sedai
Despite her lack of strength Asra is very talented. In fact like the strongest channellers (as Rand and Alivia) she is very quick in learning and doesn't need to see a weave more than once to be able to reproduce it perfectly.
Her second talent is Healing; when she was a simple Novice in the Tower, she was not instructed in the weaves used to heal, nevertheless she learned it, copying secretly the Aes Sedai performing it, and despite her weakness in the power in short time she reached a very high level of Healing.
Finally Asra has the very rare Talent that Aviendha do, of being able to tell what a weave she had never seen before would do before it is completed.