XP, also known as Experience, in the game is how you gain levels and its distribution is tightly controlled while you are on the island to allow the game to guide you through the Tutorial and stop you getting ahead of yourself too quickly.
How Much XP Do I Have
Firstly to see how much XP you have and how much to the next level, hover your mouse over the transparent and green filled curved slot below your Portrait (top left). A pop-up will display your experience level in detail for you.
Clear your Home Island
At first, you can only gain XP through completing quests found in your quest book. Later, you will use military units to clear bandit camps for adjacent sectors. Each bandit camp awards you with a certain amount of XP, depending on the units in the camp.
Adventures
At Level 26, you can play certain Adventures, and you gain XP by clearing all the bandit camps on the adventure map, as well as the Unique buildings.
Special Events
When a season event is in progress, if you are a high enough level to take part, you will probably get Adventures that are pretty easy to complete and give huge amounts of XP compared to regular Adventures for fairly small losses.