I've never thought too much about souls. I'm not religious, and without a belief in the afterlife, there's not much point in a soul.
But I don't feel particularly soulless. There are a lot of ways to describe what I'd call "my soul" - personality, ego and id, self awareness, and surely more. But for me, I'll call it my soul.
It's the part of me that's outside the narrative of my life.
If you took someone else - the most perfect method actor - and put them in my life, even with all my memories, all my experiences, and every bit of baggage that comes along with it, they wouldn't be me. I may not be a beautiful and unique snowflake (and thank you, Fight Club, for informing the opinions of many philosophically deprived, cynical young men), but I am quite specifically me. No matter how identical this double would be, how convincing, I would not become her, and she wouldn't become me. We would still be two distinct individuals, and that's where you'll find our souls.
This is functionally quite similar to the religious soul. It's a little bit personality, a little bit sheer existence, and we may differ on where it comes from, but it has the same effect. But at the end of our lives, the similarity ends. Your soul ascends to Heaven, or wherever your beliefs take you. Mine winks out, because I'll be dead. And that's an important difference. For you, the end of life is another stage in a journey. Your body is irrelevant, and your legacy isn't vital, because you still have opportunities to change, grow, and experience. For me, the end of life is the end of me, and while my body is still around (if somewhat less pleasant), I'm not. I'm gone. And what's left of me is my legacy. I'll live on in memory, or in the lives I've affected. And nowhere else.
So if I want to continue beyond my life in any way, I need to affect the world, and the people in it. Or I'll simply be gone.
Worth thinking about, at least.