Well, I suppose it depends on the context in which the word is used and the beliefs one subscribes to in interpreting the definition of spirit. Since I can't speak for anyone else, I shall give you my interpretation and opinion on who or what spirit is.
First off, the word spirit can have different meanings as I mentioned, depending on context. If we turn to Merriam-Webster for guidance, among the many definitions for spirit are:
1. :an animating or vital principle held to give life to physical organisms
: temper or disposition of mind or outlook especially when vigorous or animated <in high spirits>
: the immaterial intelligent or sentient part of a person
To me, Spirit (with a capital "S") can refer to what you might call God or Source. It is that from which we all came and to that which we all return. An energetic being, born of love and light. One of my most favorite quotes is "We are not humans having a spiritual experience, we are spiritual beings having a human experience."
Most people think of the Holy Spirit. I always wondered who or what exactly IS the Holy Spirit? If there is father (God) and son (Jesus) then where did Holy Spirit come from? Doesn't the connotation imply something bigger and all encompassing? Doesn't it sound truly Divine? Isn't it often imagined as beautiful and full of light and love? Isn't it beyond our human understanding and existence? If we religiously (for some) invoke the triad of Father, Son and Holy Spirit, then don't we acknowledge that there is an energy of sorts that is there to guide us?
Someone's spirit is akin to their soul or their essence. That energetic soup that makes them who they are. Our bodies are but vessels for our spirit while here on earth. When we die, our soul or spirit is believed to leave our bodies. Some people can sense when this is going to happen for others or even for themselves. Some people see or feel the 'spirits' of those around us, especially when someone is preparing to die.
I've never liked the term ghost. The whole idea of disembodied spirits being somehow bad and intent on scaring people and being mean and nasty just doesn't resonate with me. It's too Scooby Doo-ish! I think instead, 'ghosts' are simply spiritual beings that for one reason or another just are not ready to fully 'fly' and leave the earthly realm. They may have unfinished business here or be afraid to leave loved ones behind. Maybe they are afraid of going to the next place. Perhaps they are held here by loved ones who refuse to let them go energetically, like a rope of sorts, keeping them from flying free. Maybe they are just jokesters and are having fun playing with those still here on earth. Some may find it amusing, others may find it scary. Especially if you don't know who the 'ghost' is. Often, all you need to do is ask them what they need and give them permission to move on.
I know people who see 'dead people'. They are not crazy. They are well educated and respectable members of the community. How do you explain that? Others feel the presence of those on the other side. it may or may not be a warm and fuzzy feeling. I'm sure it can be scary. Sometimes, it's because they bring us messages. The problem is our wonderful logical human brains can't explain or make sense of it, so we make it fit into what feels good and comfortable to us and write it off as 'wishful thinking' or 'imagination' or 'coincidence'.
I really like the 4th definition. Spirit is that feeling and knowing part of you. It is what makes you, you! If only we listened to it more often...
Spirituality is simply being in touch with your own spirit and the collective spirit of love and light. Embracing who you are and from which you came. It doesn't matter what you believe, just that you have something that makes sense to you.
My hope for everyone is that they connect with their spirit and with Spirit and find their path to peace. Being open-minded and getting out of your head and into your heart is a good place to start.
If you are interested in a really good introduction to spirit, I highly recommend The Anatomy of the Spirit by Carolyn Myss. It was what started me on this journey and it is thought provoking and a worthy read for everyone, no matter what your beliefs.