You or someone else existing or being alive can represent:
Perserverance
Reliability
A purpose or activity
That person is on your mind right now for some reason
You are recognizing the life-force, Spirit, or soul within that person
For example, dreaming that someone who has passed on in your real life is alive in your dream can mean they're on your mind because you miss them or perhaps have unfinished business with them in your own mind.