WAR is a measure of how good a player is compared to a replacement level player. A zero WAR means you aren’t really providing any value to your team, but you also aren’t hurting your team. Last year, two Pittsburgh Pirates position players and nine relief pitchers finished the year with a zero fWAR.
While WAR is a good way to see how much value a player provided to a team over a season, or over a period of time, it doesn’t show how great a player was. An average player is much different to a replacement level player.