The Lord Of Embers Wiki

Naval control over provinces is visible by the factions emblem over a sea province,

Controlling sea provinces allows factions to have easier colonial wars, influence over other factions diplomacy, etc.

There are three variations of sea provinces
Neutral Province Provinces that are not governed by anyone, no battles can be fought over them, can only be claimed if you control land nearby (a land province at least 2 sea provinces away)
Claimed Province Provinces that are controlled by a faction, the faction can force others to be unable to colonize navally, trade, invade etc. Factions would have to fight for control over sea provinces if another faction will not give them access, otherwise they can come to an agreement on access and control of the provinces.
Disputed Provinces Provinces that are claimed by 2 or more factions, to gain control over the province you need to increase the amount of land border you have towards the sea province or come to an agreement with the disputed faction on who controls the province, of course naval war for control always is an option. (Note: Leaderless factions will never willingly give over sea control)

You can freely trade sea provinces between other factions as long as they can access to the ocean and a bordering land or sea border.