It's been bugging me for years. She seemed to be some kind of conscience character, and a friend surmised that she was likely a harbinger of death (notice the crows eating the bread she was holding earlier while Jacks' blood flows towards it?), but has there been any solid answer from Kurt Sutter or other writers on it? At one point in the show she had a daughter who threw a rock through the Sons' window of their ice cream shop, but then that character just disappeared.
The homeless woman was Emily Putner and she was killed in an accident that resulted from John Teller's collision with the semi-truck. Her daughter (who threw the rock at the ice cream shop) is Brooke. Brooke didn't disappear, she and Jax made peace and she became a babysitter for Abel and Thomas and had a relationship with Rat.
So what can be said for sure about Emily is that she was a ghost or spirit of some kind. Whether she was a guardian angel, an angel of death, or just a spirit who couldn't move on (etc.) is that part the Kurt Sutter has always been vague about.
My interpretation is that Jax has always been buried under the weight of the past - he idolized his father and his actions came out that. I think Emily was visual reminder of that past.