A realized gain is profit you've actually locked in by selling: sale proceeds minus the cost basis of the shares sold, minus fees. An unrealized gain is profit on paper, on shares you still hold, and it moves every time the price does. PSEye matches sells against your oldest buys first (first in, first out), which is how it decides which shares' cost basis a sale used up.
See also
See every term in the full PSE investing glossary.