Zenkai is the power boost that a Saiyan receives once he/she has
experienced near death. In the
Dragon Ball franchise, this can best be seen when Vegeta receives a large enough boost to over-power Zarbon, an enemy who had beaten him only a few episodes before.
In a much less literal
definition, anyone can experience Zenkai. It's just when someone comes back stronger and better than ever from a bad L taken in life. We all have Zenkai.