Experience
Synergy is a measure of your proficiency in a particular ship. By flying a ship you will earn synergy points for that ship. When you gain enough synergy points, you can spend it in the ship fitting screen to level up that ship. In addition to synergy with a particular ship you will also earn a small amount of "free" synergy, that can be used to level up any ship.
The higher your level in a ship, the better it will perform, gaining a small increase in statistics across the board. In addition, a certain synergy level with a ship is required to purchase the next rank of ship and advance along the ship tree.