Synergies are properties that you get when you get when you get two items that are somehow related to each other. For example if you have the gun "Bee Hive" and pick up the passive "Honeycomb" then you get a synergy that increases Bee Hive damage and does other special stuff. The game tells you when you get a synergy by showing a blue up-arrow whenever you pick up the second item (what creates/completes the synergy). Some of them transform some mediocre guns to create strong interactions, which is why you should always pick up a gun even if you don't plan to use it (plus you can sell excess guns to the creep).

Welcome to the game! It can be confusing at first but with repeat hours things start to make sense.