As you progress through Terraria you may encounter scenarios where you need more than you have. Fighting through events can help you gain items that can assist you throughout your adventure. For example, you can get the Money Trough which gives you access to a vault space independent of your inventory.
Source: terraria_logic Instagram
Many events are meant solely for upgrading your character when you are stuck. Going through events can give you access to powerful weapons and accessories which can help you progress through the game. Look through this list to understand how to summon events and which mobs start events.