Party Slot represents how many slots the ship takes up in a squadron. Like NPC parties, each squadron has 12 slots.
For example, a Y-wing has a party slot of 1, meaning that you can fit 12 Y-wings into a squadron.
A YT-1300, on the other hand, has a party slot of 4, meaning that you could only fit three of them in a squadron.
You can also combine them, so long as the total party slots of the ships you want to squad together equals 12 or less. So you can fit 2 YT-1300's and 4 Y-wings, but not 10 Y-wings and a YT-1300.
Hope this helps!