To add: the heron-marked blade is used pretty well in other ways as well.
For context for the unfamiliar readers perusing this thread: heron marks indicate a blade master — a titled earned by defeating one in single combat or by undergoing a rigorous training process over years. Rand is a farm boy given such a blade by his dad when he sets out on his journey, and he is surprised when he learns his father was a blade master because he was just a simple farmer that served in a war 20 years beforehand to satisfy his own desire for adventure.
Rand feels he does not deserve to carry the sword but does it to honor his father. Even though he trains quite a bit, it is more a crash course than a proper pedagogy. He kills a blade master at one point but there are no witnesses so by tradition he feels he can’t claim the title. He carries this imposter syndrome across many of the books and obsesses over training with the sword. This continues until he is maimed in a way that hinders his ability to fight with the blade and, at roughly the same time a character points out that it doesn’t matter if anyone saw him defeat the blade master, he earned the title and should feel confident about it.
In a lot of ways, this arc is a microcosm for his internal conflict about being the Dragon Reborn (the chosen hero of prophecy). He goes from not believing he could possibly be the Dragon, to obsessively trying to prepare himself mentally for his final confrontation with evil (he repeatedly says he must make himself as hard as steel), to eventually realizing that his own perception of what makes a Dragon / blade master is immature — both are just a men, with their own strengths and weaknesses even though they have dedicated their life to a purpose.