This is a romantic concept I used to wonder about when I was younger. I am sure I was not the only one. Many of us as a young girl must have wondered, is there such a person whom I shared my romantic past lives with, that I am meant to meet again in this lifetime?
Now that I have more knowledge of how the Universe works, I have to say this is probably more of a romantic illusion, although it cannot be completely overruled that this would never happen.
In a more general sense, all of us who live in this same era, are soul mates because we are living in the same time period and share what is going on in the world in this lifetime.
In a more intimate sense, which is probably a closer concept to the romantic illusion, we are supposed to have multiple souls around us who share several lifetimes together. So these certain groups of souls reincarnate around the same time for multiple lifetimes to learn valuable life lessons together. They are likely to be someone close to you; they may be your parents, siblings, friends, lovers or spouses.
But obviously, it is not necessarily a romantic relationship. A soul who is currently your mother in this lifetime could have been a sibling in another lifetime. A soul who is married to you in this time may have been your grandmother in another lifetime.
In addition, there is no such group of souls who will be together indefinitely. They may spend their times together for several lifetimes, but once their life lessons with you are complete, they will move on and hook up with a different group of souls.
I do think that if you did have a karmatic relationship with someone that has not been resolved, it may help you to be aware of that presence of the karma between you and that person so you may be able to try to work on it.
At any rate, it is very interesting to see who your soul mates are, think about why you met them in this lifetime and what you are supposed to learn from that relationship. At least it is one of the very reasons why I became so intrigued in learning about Akashic Records to begin with.