Neutrals are grey cities unclaimed by any player. There are two types of neutral cities:

1. Level 1 cities not conquered by any player, found on the map at the beginning of a new season or when new islands spawn.
2. Cities that belonged to players and have turned grey due to inactivity or due to resetting their season (Fresh Start).

You can conquer 30 neutral/inactive cities per day. Can be just one type or a cumulation of conquers from both types, but you can't conquer more than 30 at number.