The carriers will carry any ships you have parked in them. The carriers will also carry any alternate commanders you might have, if that commander is docked in the carrier.
If all of your commanders are docked with the carrier, they will be transported with the carrier to the next waypoint. At each stop you can leave the carrier in any ship you want and explore the area, then dock again with the carrier before it jumps to the next waypoint. You won't need to fly the distance manually if you don't want to.
Personally, I will be flying the distance myself so I can explore along the way. During the first two Distant Worlds expeditions, we didn't have fleet carriers and players had to manually fly more than a thousand jumps to reach Beagle Point with weekly meetups at different places along the way.
Shortly before the expedition starts in ~3 months, players will need to dock at one of the carriers and also transfer any other ships to it they want to bring.
As you might have gathered, there have been two previous Distant Worlds expeditions and
countless other player expeditions to other far away parts of the galaxy.
A player expedition like this is just organized cooperative gameplay. It's a long way to fly and doing it alone can be boring and lonely.
Exploring deep space with other players make it
more fun, but either way, it's exploration. You will be far away from the core star systems and unable to participate in community goals, missions or combat game play. So if you don't enjoy exploration, or prefer other aspects of the game, then you may not want to participate.
I have two accounts and one will participate in the expedition while the other stays in the bubble so I can still do other things when I'm not in the mood for exploration.