Your Diplomacy Ability reflects the amount of benefits you receive in exchange for a trade. Certain Trade Goods (Diplomatic Translators), Galactic Achievements, and Technologies improve your diplomacy ability. Some races have an intrinsic boost or penalty to diplomacy ability that is not shown in-game.
It also plays a significant role in your relations towards races: having a higher diplomacy than an opponent may help you avoid wars, become their friends, have more success toward any diplomatic option, and so on ...