It's not wonder if you haven't heard about her before (well, I would be surprised, but whatever), because she only appeared in a Japanese CD drama.
Miyamoto was a high-ranking Team Rocket member. Now she's dead. Duh. Well, maybe not all that obvious, but anyway, I'll tell you whate every other somewhat decent Team Rocket site out there says as well:
Miyamoto was Jesse's mother. The caring woman who feed her daugher snow with soy sauce *points upwards*.
Oh but Jesse loved her mother a lot. Well... of course, the anime never says that it's Miyamoto that is in the scene where Jesse gets snow rolls ("'Snow way out"), but we think it is, because the only known mother of Jesse IS named Miyamoto, and Jesse claims it was her mother, so... anyway, she was poor. Really poor (well, when you're feeding your daugher snow there isn't many other ways out), and she worked for Team Rocket. What is bizarre is that Jesse works there to "steal rare pokèmon and get rich and powerful", probably while knowing that her mother worked there, stole rare pokèmon and was still poor as a churc rat.
Um, yes, Miyamoto worked for Team Rocket, and was one of the best agents in the stable of Madam Boss (Gio's mother), and she was poor. Poor to the limit of not only feeding your daugher snow, but also going on some suicide mission to find Mew. Yah. She went to the Amazonas first (I'm not really sure what she did there, though), and after that she went back and was ordered to the Andes to find Mew.
While there she was taken by an avalance and never heard about again.
... But. I don't know if this is fan-based or actually true, but a rumor says she was saved by an Articuno and started a new life as Lorelei of Elite Four. Which would mean that Misty has a crush on Jesse mother... and that Professor Ivy is her aunt! (me and my theories...)
But as I said, it's just something I heard. It's still a nice thought, isn't it?