Party Finder is a feature that allows you to connect with players from different servers to you or as a way of having a 'private' server without needing to click on any links.
This feature can be used as a way for new players to have support without having to rely on having friends or being in a community to progress in Ultimate Tower Defense. It is also useful for players to find trades.
How to use Party Finder?
Click the Party Finder icon on the right side of your game screen. It looks like this: 
You can join a party or create your own server and then advertise.
This is what the server advertising menu looks like: 
You can choose a category, server name, and level/elo requirements for your server. Once you click "Advertise Server" at the bottom of the menu, it will become visible to other players.
If you are the owner of a party finder server, you have the option to kick players by using the Manage button on the top right of the "My Server" page. When you ban a player from your server, they cannot rejoin for 10 minutes unless the owner leaves.
This is what the Manage button looks like: 
If you are in a party server and then play infinity castle, when that match ends you will be sent back to a public lobby instead of returning to the party server.